A meshless method for solving the Euler system of equations for the inviscid gas flow in a three-dimensional space is described in detail. Polynomial Least Squares approximation of partial spatial derivatives of gas-dynamic parameters and the transformation of an orthonormal coordinate system are used for calculating the fluxes between the computational nodes.

The paper deals with the computational realization of the mathematical model of switching dynamics of ReRAM elements based on the system of equations of drift-diffusion of ions, electrical conductivity and thermal conductivity in the element.

The paper deals with the numerical solution of fractional differential equations with interval parameters in terms of derivatives describing anomalous diffusion processes. Computational algorithms for solving initial–boundary value problems as well as the corresponding inverse problems for equations containing interval fractional derivatives with respect to time and space are presented. The algorithms are based on the previously developed and theoretically substantiated adaptive interpolation algorithm tested on a number of applied problems for modeling dynamical systems with interval parameters; this makes it possible to explicitly obtain parametric sets of states of dynamical systems. The efficiency and workability of the proposed algorithms are demonstrated in several problems.

In their previous work [1], the authors presented a method of identifying the characteristics of a gaseous medium from measurements of the heat flux absorbed by the surface of a blunt body in a gas flow. The identification problem was stated in an extreme formulation: the sought-for transport properties of a gaseous medium were determined via minimization of the objective function of the estimated and measured heat fluxes absorbed by the surface of a solid body. For minimization of the objective function, the Nelder–Mead method was used in combination with random restarts; the results of testing the algorithm in a model experiment are given. This paper presents the technique of conduction of experiment to verify the method for identification of the gas flow parameters. Experimental results are given for two different gas flow sources.

Важную роль при построении математических моделей динамических систем играют обратные задачи, к которым, в частности, относится задача параметрической идентификации. В отличие от классических моделей, оперирующих точечными значениями, интервальные модели дают ограничения сверху и снизу на исследуемые величины. В работе рассматривается интерполяционный подход к решению интервальных задач параметрической идентификации динамических систем для случая, когда экспериментальные данные представлены внешними интервальными оценками. Цель предлагаемого подхода заключается в нахождении такой интервальной оценки параметров модели, при которой внешняя интервальная оценка решения прямой задачи моделирования содержала бы экспериментальные данные или минимизировала бы отклонение от них. В основе подхода лежит алгоритм адаптивной интерполяции для моделирования динамических систем с интервальными неопределенностями, позволяющий в явном виде получать зависимость фазовых переменных от параметров системы. Сформулирована задача минимизации расстояния между экспериментальными данными и модельным решением в пространстве границ интервальных оценок параметров модели. Получено выражение для градиента целевой функции. На репрезентативном наборе задач продемонстрированы эффективность и работоспособность предлагаемого подхода.

The issues of parametric identification of fractional differential models describing the processes of anomalous diffusion/heat conductivity are considered. The emphasis is on the option with a spatially localized initial condition; this corresponds to the experimental approach to determining diffusion characteristics. Methods are proposed for solving the identification problem that do not require repeated solution of the direct problem. Testing the methods has been carried out in a quasireal experiment mode.

Correlations for calculation of heat loads during a return of spacecraft at the second cosmic velocity are given. Analysis of the heat transfer for a model descent trajectory has been carried out. The convective and radiative heat fluxes, the relative heat transfer coefficient, and the radiative-equilibrium surface temperature have been calculated. The results obtained are a basis for design and optimization of the heat shield of spacecraft.

The issues of simulation modeling of an analog impulse neural network based on memristive elements in the problem of pattern recognition are studied. Simulation modeling allows us to configure the network at the level of a mathematical model, and subsequently use the obtained parameters directly in the process of operation. The network model is given as a dynamic system, which can consist of tens or hundreds of thousands of ordinary differential equations. Naturally, there is a need for an efficient and parallel implementation of an appropriate simulation model. Open multiprocessing (OpenMP) is used as the technology for parallelizing calculations, since it allows us to easily create multithreaded applications in various programming languages. The efficiency of parallelization is evaluated on the problem of modeling the process of training the network to recognize a set of five images of a size of 128 by 128 pixels, which leads to the solution of about 80 000 differential equations. In this problem, the calculations are accelerated by a factor of over six. According to the experimental data, the operating character of memristors is stochastic, as shown by the scatter in the current-voltage characteristics (VACs) when switching between high-resistance and low-resistance states. To take this feature into account, a memristor model with interval parameters is used, which gives upper and lower limits on the values of interest, and encloses the experimental curves in corridors. When simulating the operation of the entire analog self-learning impulse neural network, in each epoch of training, the parameters of the memristors are set randomly from the selected intervals. This approach makes it possible to dispense with the use of a stochastic mathematical apparatus, thereby further reducing computational costs.

The effect of an outside wave impact on filtration of fluids from capillaries into environmental porous media and back is considered. Two mechanisms of filtration acceleration are found. The first of them is specified with changing the permeability of environmental porous media and the surface layer of capillaries due to the wave impact. The second mechanism is caused by synchronous and in-phase vibrations of pressure in the capillary and the permeability of environmental porous media. It manifests itself only in the resonance case. Both these effects can be used for intensification of the trance-capillary exchange in medicine.

Рассматривается влияние внешнего волнового воздействия на фильтрацию жидкостей из капилляров в окружающую капилляры ткань и из ткани в капилляры. Установлены два механизма увеличения скорости фильтрации: нерезонансный, связанный с несимметричностью изменения проницаемости поверхностного слоя капилляров и окружающей капилляр ткани на смежных полупериодах волновых воздействий и резонансный, связанный с увеличением перепада давлений, обусловленного пульсовой волной в капилляре, синхронного и синфазного с ним повышения проницаемости, обусловленного волновыми воздействиями. Установленные эффекты могут найти применение в медицине для интенсификации транскапиллярного обмена и микроциркуляции в кровеносной системе.

Microelectronics is one of the industries that have been developing at a record pace in recent decades. The most important role in the development of the digital economy is played by the development and organization of the production of a new generation of microelectronic sensors of external influences and microsystems based on them. Due to the need to operate such devices under various conditions, including wide temperature ranges, determining the ranges of their reliable operation is an urgent task. Thermal studies are carried out using the previously constructed two-level mathematical model of a Hall field sensor (HFS) based on a silicon-on-insulator (SOI) heterostructure. The results of computational and experimental studies of the influence of temperature on the characteristics of the SOI HFS are presented. The possibility of operation of the sensor in a wide temperature range is shown. Parametric identification of the mathematical model developed by the authors based on the experimental data is carried out. The sensitivity function of the electric current to temperature change is determined. The proposed approach makes it possible to estimate the required sensitivity of the sensor to determine the temperature with the given accuracy.

The parametric identification problem for dynamical systems with rectangular and ellipsoid parameter uncertainty domains is solved for the case in which the experimental data are given in the form of intervals. The state of the considered dynamical systems at each moment of time is a parametric set. An objective function that characterizes the degree of deviation of the parametric sets of states from experimental interval estimates is constructed in the space of parameter uncertainty domains. To minimize the objective function, a sliding window algorithm has been developed, which is related to gradient methods. It is based on an adaptive interpolation algorithm that allows one to explicitly obtain parametric sets of states of a dynamical system within a given parameter uncertainty domain (window). The efficiency and performance of the proposed algorithm are demonstrated.

Int this paper, we study the process of changing the polarization of hafnium oxide crystals in the orthorhombic phase associated with the gradual weakening of polarization effects in FeRAM elements based on thin films of hafnium oxide HfO2. To solve the problem, quantum mechanical calculations of the structure of orthorhombic hafnium oxide are performed, a possible way of crystal restructuring during a change in polarization when a voltage is applied is identified, and its optimization is carried out using the elastic band method. The values of the change in polarization and the energy barrier of the corresponding transition are obtained. The stability of this transition is studied. The results of a series of computational experiments using high-performance computing systems of hybrid architecture based on the Center for Collective Use at the Federal Research Center “Computer Science and Control” are presented. An analysis of the results shows that, despite the low energy barrier of the transition, the probability of a spontaneous change in polarization is low due to the impossibility of changing the polarization of an individual cell with no allowance for the effect of the polarizations of the neighboring cells.

The influence of external wave action on the filtration of the fluid from capillaries into the tissue surrounding the capillaries and from the tissue into the capillaries is considered. Two mechanisms for increasing the filtration rate are established: nonresonant, associated with the asymmetry of the change in the permeability of the capillary surface layer and the tissue surrounding the capillary at adjacent half-periods of wave actions, and resonant, associated with an increase in the pressure drop caused by a pulse wave in the capillary, and a synchronous and in-phase increase in permeability due to wave actions. The established effects can find application in medicine for the intensification of transcapillary exchange and microcirculation in the circulatory system.

The parametric identification problem for dynamical systems with rectangular and ellipsoid parameter uncertainty domains is solved for the case in which the experimental data are given in the form of intervals. The state of the considered dynamical systems at each moment of time is a parametric set. An objective function that characterizes the degree of deviation of the parametric sets of states from experimental interval estimates is constructed in the space of parameter uncertainty domains. To minimize the objective function, a sliding window algorithm has been developed, which is related to gradient methods. It is based on an adaptive interpolation algorithm that allows one to explicitly obtain parametric sets of states of a dynamical system within a given parameter uncertainty domain (window). The efficiency and performance of the proposed algorithm are demonstrated.

We present an approach to solving parametric identification problems for dynamical systems. The approach is aimed at finding an interval estimate of the model parameters in which the solution of the corresponding modeling problem would contain the initial (experimental) data or minimize the deviation from them. The approach is based on an earlier-developed, tested, and justified adaptive interpolation algorithm for modeling dynamical systems with interval parameters. The problem of minimizing the distance between the solution of the interval problem and the experimental values of the phase variables in the space of bounds of the interval estimates of the model parameters is formulated. An expression for the gradient of the objective function to be minimized is obtained for further application of first-order optimization methods. The proposed approach is tested on a representative set of problems.

This paper considers the features of solving the problem identifying characteristics of a gaseous medium via measurements of the heat flux absorbed by the surface of a blunt body in a supersonic flow. Three groups of parameters are distinguished identification of which is feasible from known values of surface temperature and heat flux: thermodynamic properties of the gaseous medium, its transport properties and conditions on the outer boundary of the boundary layer. In this paper, the transport properties of the gaseous medium are considered as an object of identification. The study is carried out within the framework of the perfect gas model. The identification problem is formulated in the extremum setting. For optimization, the Nelder–Mead method is used in combination with random restarts. It is shown that owing to the specificity of the structure of a set of points the objective function value in which is lower than the value specified by the accuracy of the heat flux measurements, it is possible to obtain a fairly accurate estimate of the identified parameters.

Multiscale approaches, models and algorithms for designing neuromorphic devices for the memory of new generation computers are presented. The developed approaches make it possible to solve problems associated with simulating modeling of the work of neuromorphic networks in intellectual analysis modes of data and machine learning. The issues related to the construction of a computing model of formation/destruction of conductive channels in memristive elements underlying neuromorphic networks are considered. New algorithms for modeling the work of the neuromorphic network have been created, taking into account stochastic effects, as well as original methods and means of simulating modeling of teaching a neuromorphic network. The main approaches are presented when creating software for simulating modeling of neuromorphic networks based on the integration platform of multiscale modeling, combining information flows at various large -scale levels, including the level of a new resistive memory element, the level of neuromorphic network and the level of simulation of the neuromorphic network on precedents . The book is intended for scientists, specialists in the field of computing electronics, senior students and graduate students of technical universities.