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Location-based models — one of areas of CAMA (computer-assisted mass apriasal) building. When taking into account the location of the object using spatial autoregressive models structure of models (type of spatial autocorrelation, choice of “nearest neighbors”) cannot always be determined before its construction. Moreover, in practice there are situations where more efficient methods are taking into account different rates depending on the type of the object from its location. In this regard there are important issues in spatial methods area:

– fields of methods efficacy;

– sensitivity of the methods on the choice of the type of spatial model and on the selected number of nearest neighbors.

This article presents a methodology for assessing the effectiveness of computer evaluation of real estate objects. There are results of approbation on methods based on location information of the objects.

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.

A new method for calculating the initiation and development of narrow local damage zones in specimens and structural elements subjected to various modes cyclic loadings is proposed based on multi regime two criteria model of fatigue fracture. Such narrow zones of damage can be considered as quasi-cracks of two different types, corresponding to the mechanism of normal crack opening and shear.

Numerical simulations that are aimed to reproduce the left and right branches of the full fatigue curves for specimens made from titanium and aluminum alloy and to verify the model. These branches were constructed based on tests results obtained under various modes and cyclic loading schemes. Examples of modeling the development of quasi-cracks for two types (normal opening and shear) under different cyclic loading modes for a plate with a hole as a stress concentrator are given. Under a complex stress state in the proposed multi regime model, a natural implementation of any considered mechanisms for the quasi-cracks development is possible. Quasi-cracks of different types can develop in different parts of the specimen, including simultaneously.

A large number of methods have been developed to solve the Navier – Stokes equations in the case of incompressible flows, the most popular of which are methods with velocity correction by the SIMPLE algorithm and its analogue — the method of splitting by physical variables. These methods, developed more than 40 years ago, were used to solve rather simple problems — simulating both stationary flows and non-stationary flows, in which the boundaries of the calculation domain were stationary. At present, the problems of computational fluid dynamics have become significantly more complicated. CFD problems are involving the motion of bodies in the computational domain, the motion of contact boundaries, cavitation and tasks with dynamic local adaptation of the computational mesh. In this case the computational mesh changes resulting in violation of the velocity divergence condition on it. Since divergent velocities are used not only for Navier – Stokes equations, but also for all other equations of the mathematical model of fluid motion — turbulence, mass transfer and energy conservation models, violation of this condition leads to numerical errors and, often, to undivergence of the computational algorithm.

This article presents an implicit method of splitting by physical variables that uses divergent velocities from a given time step to solve the incompressible Navier – Stokes equations. The method is developed to simulate flows in the case of movable and contact boundaries treated in the Euler paradigm. The method allows to perform computations with the integration step exceeding the explicit time step by orders of magnitude (Courant – Friedrichs – Levy number $CFL\gg1$). This article presents a variant of the method for incompressible flows. A variant of the method that allows to calculate the motion of liquid and gas at any Mach numbers will be published shortly. The method for fully compressible flows is implemented in the software package FlowVision.

Numerical simulating classical fluid flow around circular cylinder at low Reynolds numbers ($50 < Re < 140$), when laminar flow is unsteady and the Karman vortex street is formed, are presented in the article. Good agreement of calculations with the experimental data published in the classical works of Van Dyke and Taneda is demonstrated.

In the presented work, a hybrid optimal simulation model of an assembly shop in the AnyLogic environment has been developed, which allows you to select the parameters of production systems. To build a hybrid model of the investigative approach, discrete-event modeling and aggressive modeling are combined into a single model with an integrating interaction. Within the framework of this work, a mechanism for the development of a production system consisting of several participants-agents is described. An obvious agent corresponds to a class in which a set of agent parameters is specified. In the simulation model, three main groups of operations performed sequentially were taken into account, and the logic for working with rejected sets was determined. The product assembly process is a process that occurs in a multi-phase open-loop system of redundant service with waiting. There are also signs of a closed system — scrap flows for reprocessing. When creating a distribution system in the segment, it is mandatory to use control over the execution of requests in a FIFO queue. For the functional assessment of the production system, the simulation model includes several functional functions that describe the number of finished products, the average time of preparation of products, the number and percentage of rejects, the simulation result for the study, as well as functional variables in which the calculated utilization factors will be used. A series of modeling experiments were carried out in order to study the behavior of the agents of the system in terms of the overall performance indicators of the production system. During the experiment, it was found that the indicator of the average preparation time of the product is greatly influenced by such parameters as: the average speed of the set of products, the average time to complete operations. At a given limitation interval, we managed to select a set of parameters that managed to achieve the largest possible operation of the assembly line. This experiment implements the basic principle of agent-based modeling — decentralized agents make a personal contribution and affect the operation of the entire simulated system as a whole. As a result of the experiments, thanks to the selection of a large set of parameters, it was possible to achieve high performance indicators of the assembly shop, namely: to increase the productivity indicator by 60%; reduce the average assembly time of products by 38%.

Based on the Holstein Hamiltonian, the dynamics of the charge introduced into the molecular chain of sites was modeled at different temperatures. In the calculation, the temperature of the chain is set by the initial data ¡ª random Gaussian distributions of velocities and site displacements. Various options for the initial charge density distribution are considered. Long-term calculations show that the system moves to fluctuations near a new equilibrium state. For the same initial velocities and displacements, the average kinetic energy, and, accordingly, the temperature of the T chain, varies depending on the initial distribution of the charge density: it decreases when a polaron is introduced into the chain, or increases if at the initial moment the electronic part of the energy is maximum. A comparison is made with the results obtained previously in the model with a Langevin thermostat. In both cases, the existence of a polaron is determined by the thermal energy of the entire chain.

According to the simulation results, the transition from the polaron mode to the delocalized state occurs in the same range of thermal energy values of a chain of $N$ sites ~ $NT$ for both thermostat options, with an additional adjustment: for the Hamiltonian system the temperature does not correspond to the initially set one, but is determined after long-term calculations from the average kinetic energy of the chain.

In the polaron region, the use of different methods for simulating temperature leads to a number of significant differences in the dynamics of the system. In the region of the delocalized state of charge, for high temperatures, the results averaged over a set of trajectories in a system with a random force and the results averaged over time for a Hamiltonian system are close, which does not contradict the ergodic hypothesis. From a practical point of view, for large temperatures T ≈ 300 K, when simulating charge transfer in homogeneous chains, any of these options for setting the thermostat can be used.

The study of the mechanism for the development of mass panic in view of its extreme importance and social danger is an important scientific task. Available information about the mechanism of her development is based mainly on the work of psychologists and belongs to the category of inaccurate. Therefore, the theory of fuzzy sets has been chosen as a tool for developing a mathematical model of a person's susceptibility to panic situations. As a result of the study, an fuzzy model was developed, consisting of blocks: “Fuzzyfication”, where the degree of belonging of the values of the input parameters to fuzzy sets is calculated; “Inference” where, based on the degree of belonging of the input parameters, the resulting function of belonging of the output value to an odd model is calculated; “Defuzzyfication”, where using the center of gravity method, the only quantitative value of the output variable characterizing a person's susceptibility to panic situations is determined Since the real quantitative values for linguistic variables mental properties of a person are unknown, then to assess the quality of the developed model, without endangering people, it is not possible. Therefore, the quality of the results of fuzzy modeling was estimated by the calculated value of the determination coefficient R2, which showed that the developed fuzzy model belongs to the category of good quality models $(R^2 = 0.93)$, which confirms the legitimacy of the assumptions made during her development. In accordance with to the results of the simulation, human susceptibility to panic situations for sanguinics and cholerics can be attributed to “increased” (0.88), and for phlegmatics and melancholics — to “moderate” (0.38). This means that cholerics and sanguinics can become epicenters of panic and the initiators of stampede, and phlegmatics and melancholics — obstacles to evacuation routes. What should be taken into account when developing effective evacuation measures, the main task of which is to quickly and safely evacuate people from adverse conditions. In the approved methods, the calculation of normative values of safety parameters is based on simplified analytical models of human flow movement, because a large number of factors have to be taken into account, some of which are quantitatively uncertain. The obtained result in the form of quantitative estimates of a person's susceptibility to panic situations will increase the accuracy of calculations.

Images of surface topography of ultrathin magnetic films have been used for Monte Carlo simulations in the framework of the ferromagnetic Ising model to study the hysteresis and thermal properties of nanomaterials. For high performance calculations was used super-scalable parallel algorithm for the finding of the equilibrium configuration. The changing of a distribution of spins on the surface during the reversal of the magnetization and the dynamics of nanodomain structure of thin magnetic films under the influence of changing external magnetic field was investigated.

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.