Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 729
Model of porous material sintering
Статья научная
The mathematical model of inert porous materials sintering was proposed. As an initial data, the model uses the initial distribution of pore surface elements and time-temperature conditions of sintering. Sintering is modelled by the system of kinetic equations describing shrinkage of a material depending on its initial properties and a time-temperature condition of the process. Experiments on aluminum oxide powder sintering have been carried out in several time-temperature conditions in which linear shrinkage was traced in time. The initial powder particles size distribution was previously measured. A value of main parameters used in the model was determined according to the sample linear shrinkage data measured at the 10 C/min heating rate. Time dependences of linear shrinkage were calculated for the heating rates of 5 and 15 C/min. Comparison of the calculated dependences with experimental data for heating rates 5 and 15 С/min has shown the good qualitative and quantitative concordance.
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Статья научная
In this paper we studied the possibilities of adaptation of Scilab freeware computer mathematic package to the solution of special calculation problems are studied. We modeled and calculated the family of adaptive devices of automation, control and protection for smart/intellectual electric grids including renewable energy sources. We studied the possibilities of Scilab package for sequential calculating using a big number of algebraic functions, solving the systems of linear algebraic equations, analyzing of results, solving the tasks of optimization, building 2D and 3D function diagrams, etc. All calculated solutions obtained from Scilab, were analysed in comparison with the similar solutions calculated in MathCAD. The results confirm the relevance of using the Scilab package for these purposes and demonstrate some of its advantages in education, scientific research and electric engineering calculations.
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Modelling of "green" investments risks
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The practical lack of methods for quantitative assessment of capital-intensive renewable energy projects taking into account the present uncertainty leads to an increase in the riskiness and reduce the amount of "green" investment in the economy. It resolves the urgency of the developing approaches to the renewable energy projects assessment. The article presents the diagnostics of specific risks and assessment of limiting the investor market share in the renewable energy projects with the optimal risk level. The proposed authors' approach to risks formalization of renewable energy deals is based on the introduction of dummy-variable, evaluation of coefficients' significance, tendency and strength of relation of risks indicators. This approach yields an indicative assessment of the deals' riskiness taking into account sectoral specifics. The developed method to limiting the investor market share is based on the principles of the economic capital theory. It allows for consolidating the current states of investor, project and economy. Research veracity is confirmed by the practical implementation. The results of the study can be used by the management of energy companies, investors and analysts in making financial decisions.
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The aim of this work is to carry out numerical calculation of electric fields in axisymmetric systems for cathode protection of underground structures against corrosion. As is known, cathode protection is a complex multi-parameter system, which has a number of features depending on the type and form of the protected structure, properties of the surrounding environment, etc. As a result, the modelling of protection parameters is quite complex and requires new more advanced computer technologies. In this work, we construct a mathematical model of the problem on the electric field distribution in an axisymmetric system for cathode electrochemical protection of underground structures. In addition, we propose an algorithm to solve the problem. The algorithm is based on the use of integral Green transformations and, in particular, the second Green integral formula. Also, we give an example of a computer implementation of the proposed algorithm in the case of a homogeneous half-space. The Scilab application package is used to implement the example.
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Статья научная
The paper considers a boundary-value problem for a hybrid system of differential equations, which represents a generalized mathematical model for a system of interconnected rigid bodies attached to the rod by elastic-damping links. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. For the theoretical foundations of our approach to investigation of the boundary value problem for the hybrid system of differential equations we propose a method of finding eigenvalues for the boundary-value problem. The comparative analysis of the results of numerical computations conducted with the use of the proposed method and the results obtained by other techniques known from the literature have proved the validity and the universal character of the proposed approach.
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Modelling of the axisymmetric precision electrochemical shaping
Статья научная
The problem on modelling of a precision shaping and boundary conditions are formulated according to Faraday's law and with applying of stepwise dependence current efficiency on current density. The problem is reduced to the solution of a boundary problem for definition of two analytical functions of the complex variable. The first function is a conformal mapping of region of parametrical variable on the physical plane. In order to determine this function we use the Schwartz's integral and a spline interpolation. Unlike a plane problem for determination of potential and stream function of an axisymmetric field, the integration transformations of the second analytical function are used. The analytical function is defined in the form of a sum of two addends. The first addend takes into account the singularities of the function so that the second addend has no singularities. The second function is defined by the Schwartz's integral. Interpolation by spline functions is carried out, where the spline coefficients are derivatives of these functions by means of which the intensity vector components are calculated. We propose the method to solve the axisymmetric stationary problems, which differs from the known methods by the accuracy. By means of the method, we obtain the numerical results, describing the workpiece form. The error estimation of the obtained results is carried out. Also, we show qualitative coincidence with results of plane problem solution.
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Modelling of the time series digressions by the example of the ups of the Ural
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The article oversees forecasting model for deviations of the balancing market index and day-ahead market index according to the maximum similarity sample for different levels of approximation in the context of positive and negative time-series value. The model is being tested on the factual data of the Integrated Power system of the Ural, Wholesale market for electricity and power of the Russian Federation. The offered model is based on the sample of maximum similarity of the daily digressions by "Day-ahead" market from balancing market index in the history data of 2009 - 2014 that was acquired from an official web-site of the wholesale electric power market. Testing of the mathematical model gave the prediction error of 3,3%. The offered toolkit for forecasting of the main day-ahead and balancing market parameters is recommended to use for operational work of the industrial enterprise.
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Modelling the flow of character recognition results in video stream
Статья научная
The paper considers problems of developing stochastic models consistent with results of character image recognition in video stream. A set of assumptions that define the models structure and properties is stated. A class of distributions, namely the Dirichlet distribution and its generalizations, that set a description of the model components is pointed out; and methods for statistical estimation of the distribution parameters are given. To rank the models, the Akaike information criterion is used. The proposed theoretical distributions are verified vs sample data.
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Modelling the human papilloma virus transmission in a bisexually active host community
Статья научная
In this article, we construct a mathematical model describing the transmission dynamics of Human Papilloma Virus (HPV) in a bisexually active host community. Comprehensive mathematical techniques are used to qualitatively and quantitatively analyze the model. We analyze the local and global stabilities of the model's equilibria and show that if the basic reproduction number is less than unity, then the model is locally and globally asymptotically stable at the HPV-free static states. Also, if the basic reproduction number is less than unity, then the HPV-endemic static state is globally asymptotically stable. Numerical simulations are carried out and graphical illustrations are presented to validate the theoretical results.
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Modelling the innovation activity of an enterprise
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Specific features of foresight expert forecasting methods make them ineffective for compresided analysis of enterprise innovation activity. This determined the urgency of developing a deterministic method for predicting the results of innovative activities of the corporation resulting from the simulation of production indicators. The paper considers modelling of innovation process quantitative characteristics, aimed at the industrial enterprises innovative activity evaluation under implementation of a specific investment project. In the process of modelling operations used a production function. To account for the specificity of industrial production basic production function modified with regard to material resources and influence of "autonomous" technical progress is Hicks-neutral. The developed algorithm of solution the Mendershausen multicollinearity effect. Credibility built industrial plant test confirmed by the consent of the criteria of operational models. The author's method of estimation of innovative activity of industrial enterprises in implementation of innovation project on the basis of dynamics of indicators of the elasticity of production. The proposed method allows to reflect the economic result from the introduction of a specific innovation project. The research results are recommended for practical use in the selection of investment projects and for integrated assessment of corporate governance through the additional key performance indicator.
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Modelling the process of non-equilibrium hydrate formation in a porous reservoir
Статья научная
This paper presents a solution to the flat-dimensional problem of gas hydrate formation in a porous medium. Highly permeable reservoirs are considered, as a result of which it is assumed that the process accompanied by the transition of gas into the hydrate composition is nonequilibrium. Based on the numerical solution, the influence of injection pressure and formation permeability on the peculiarities of phase transitions process has been studied. It is shown that with an increase in the injection pressure, both the maximum possible temperature of the system and the length of the hydrate-containing region increase. It has been found that the maximum temperature realized in the system, depending on the permeability of the reservoir, has a non-monotonic character. The influence of the initial temperature of the porous reservoir on the dynamics of phase transitions has been studied.
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Models and methods for three external ballistics inverse problems
Статья научная
We consider three problems of selecting optimal gun barrel direction (or those of selecting optimal semi-axis position) when firing an unguided artillery projectile on the assumption that the gun barrel semi-axis can move in a connected nonconvex cone having a non-smooth lateral surface and modelling visibility zone restrictions. In the first problem, the target is in the true horizon plane of the gun, the second and the third problems deal with some region of 3D space. A distinctive feature of the models is that the objective functions are e-Lipschitz ones. We have constructed a unified numerical method to solve these problems based on the algorithm of projecting a point onto e-Lipschitz level function set. A computer programme has been based on it. А series of numerical experiments on each problem has been carried out.
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Models and methods of computer-aided design of the user interface of software systems
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The article deals with the design, mathematical modeling and development of the prototype of the interface of the information system of the audit fund. In this paper, the study of the design of the user interface, methods for creating interfaces, user interaction types, a list of the functionality of the system, a mathematical model, nondeterministic finite automaton (NFA) was built user interaction with system elements and a prototype of the system have been created. According to the authors, this system will automate and simplify the process of managing the audit fund, joint use of the NFA and one of the methods of creating interfaces, namely, ontology will allow describing domain concepts, edit domain concepts, generate databases and knowledge bases, broadcast from one language to another, get rid of information redundancy, reduce time for database development as well as simplify the process of scheduling the university.
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Статья научная
At the application of bifurcation theory methods to nonlinear boundary value problems for ordinary differential equations of the fourth and higher order there usually arise technical difficulties, connected with determination of bifurcation manifolds, spectral investigation of the direct and conjugate linearized problems and the proof of their Fredholm property. For overcoming of this difficulty here the roots separation method is applied to the relevant characteristic equations with subsequent presentation of critical manifolds, that allows to investigate nonlinear problems in the precise statement. Such approach is applied here to two-point boundary value problem for the nonlinear ODE of the fourth order describing the buckling (divergence) of an elongated plate in a supersonic flow of gas, subjected to compressed or extended boundary stresses at the various boundary fastenings.
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Статья научная
Sobolev type equations theory has been an object of interest in recent years, with much attention being devoted to deterministic equations and systems. Still, there are also mathematical models containing random perturbation, such as white noise. A new concept of "white noise", originally constructed for finite dimensional spaces, is extended here to the case of infinite dimensional spaces. The main purpose is to develop stochastic higher-order Sobolev type equations theory and provide some practical applications. The main idea is to construct "noise" spaces using the Nelson-Gliklikh derivative. Abstract results concerning initial-final problems for higher order Sobolev type equations are applied to the Boussinesq-Love model with additive "white noise". We also use well-known methods in the investigation of Sobolev type equations, such as the phase space method, which reduces a singular equation to a regular one, as defined on some subspace of the initial space.
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Multipoint initial-final value problem for the model of Devis with additive white noise
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The evolution of the free surface of the filtering fluid in a reservoir of limited power is modeled by the Davis equation with homogeneous Dirichlet conditions. Depending on the nature of the free term describing the internal source of the liquid, the model will be deterministic or stochastic. The deterministic model has been studied in various aspects by many researchers with different initial (initial-final value conditions). The stochastic model is studied for the first time. The main result is the proof of the unique solvability of the evolutionary model with an additive white noise and a multipoint initial-final value condition.
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Neural net decoders for linear block codes
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The work is devoted to neural network decoders of linear block codes. Analytical methods for calculating synaptic weights based on a generator and parity-check matrices are considered. It is shown that to build a neural net decoder based on a parity-check matrix was sufficiently four layers feedforward neural net. The activation functions and weight matrices for each layer are determined, as well as the number of weights for the neural net decoder. An example of error correction with uses of the BCH neural net decoder is considered. As a special case of a neural network decoder built on the basis of a parity-check matrix, a model for decoding Hamming codes has been proposed. This is the two-layer feedforward neural net for with a neuron number equal to the length of the codeword and a number of weight coefficients equal to the square of the codeword length. The graphs of the number of a synaptic weight of neural net decoders based on the generator and parity-check matrices, on the number of bits and the number of corrected errors, are shown.
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In this paper, we present two new P-type and D-type iterative learning control (ILC) update laws for linear stochastic systems with random data dropout modeled with a Bernoulli random variable. We prove that the P-type and D-type ILC update laws converge to the desired input in the almost sure sense. We show that the convergence conditions of the inputs corresponding to the P-type and D-type ILC update laws for networked control systems are the same. We present the performance comparison of the P-type and D-type ILC update laws. In this comparison, we conclude that the P-type ILC update law is more effective than the D-type ILC update law for networked control systems.
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New approximate method for solving the Stokes problem in a domain with corner singularity
Статья научная
In this paper we introduce the notion of an Rv-generalized solution to the Stokes problem with singularity in a two-dimensional non-convex polygonal domain with one reentrant corner on its boundary in special weight sets. We construct a new approximate solution of the problem produced by weighted finite element method. An iterative process for solving the resulting system of linear algebraic equations with a block preconditioning of its matrix is proposed on the basis of the incomplete Uzawa algorithm and the generalized minimal residual method. Results of numerical experiments have shown that the convergence rate of the approximate Rv-generalized solution to an exact one is independent of the size of the reentrant corner on the boundary of the domain and equals to the first degree of the grid size h in the norm of the weight space W12,v(Ω) for the velocity field components in contrast to the approximate solution produced by classical finite element or finite difference schemes convergence to a generalized one no faster than at an O(hα) rate in the norm of the space W12(Ω) for the velocity field components, where α
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New features of parallel implementation of N-body problems on GPU
Статья научная
This paper focuses on the parallel implementation of a direct N-body method (particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered for models with a number of particles N:105-107. By means of N-body simulations of gravitationally unstable stellar galactic we have investigated the algorithms parallelization efficiency for various Nvidia Tesla graphics processors (K20, K40, K80). Particular attention was paid to the parallel performance of simulations and accuracy of the numerical solution by comparing single and double floating-point precisions (SP and DP). We showed that the double-precision simulations are slower by a factor of 1,7 than the single-precision runs performed on Nvidia Tesla K-Series processors. We also claim that application of the single-precision operations leads to incorrect result in the evolution of the non-axisymmetric gravitating N-body systems. In particular, it leads to significant quantitative and even qualitative distortions in the galactic disk evolution. For instance, after 104 integration time steps for the single-precision numbers the total energy, momentum, and angular momentum of a system with N=220 conserve with accuracy of 10-3, 10-2 and 10-3 respectively, in comparison to the double-precision simulations these values are 10-5, 10-15 and 10-13, respectively. Our estimations evidence in favour of usage of the second-order accuracy schemes with double-precision numbers since it is more efficient than in the fourth-order schemes with single-precision numbers.
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