Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp
Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 838
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
Nonlinear conjugate gradient algorithm is highly effective for optimization due to its low storage requirements and simple structure properties. Expanding on the Barzilai and Borwein conjugate gradient method, we propose a three-term conjugate gradient method with a restart procedure for unconstrained optimization. This method ensures global convergence under standard assumptions and employs a standard Wolfe line search. To evaluate its performance, we carry out comprehensive numerical experiments for large scales to address challenges in unconstrained optimization and image restoration. The numerical results prove that the new method is more effective compared to other classical methods.
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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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Статья научная
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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Статья научная
In this paper, we prove some new results on operational second order differential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is performed when the second member belongs to a Sobolev space. Existence, uniqueness and optimal regularity of the classical solution are proved using interpolation theory and results on the class of operators with bounded imaginary powers. We also give an example to which our theory applies. This paper improves naturally the ones studied in the commutative case by M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri: in fact, introducing some operational commutator, we generalize the representation formula of the solution given in the commutative case and prove that this representation has the desired regularity.
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Non-Uniqueness of Solutions to Boundary Value Problems with Wentzell Condition
Статья научная
Recently, in the mathematical literature, theWentzell boundary condition is considered from two points of view. In the first case, let us call it classical one, this condition is an equation containing a linear combination of the values of the function and its derivatives on the boundary of the domain. Moreover, the function itself also satisfies the equation with an elliptic operator defined in the domain. In the second case, which we call neoclassical one, the Wentzell condition is an equation with the Laplace–Beltrami operator defined on the boundary of the domain understood as a smooth compact Riemannian manifold without boundary, and the external action is represented by the normal derivative of a function defined in the domain. The paper shows the non-uniqueness of solutions to boundary value problems with the Wentzell condition in the neoclassical sense both for the equation with the Laplacian and for the equation with the Bi-Laplacian given in the domain.
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Статья научная
Degenerate differential equations, as part of the differential-algebraic equations, the last few decades cause increasing interest among researchers, both because of the attractiveness of the considered theoretical questions, and by virtue of their applications. Currently, advanced methods developed in this area are used for system modelling and analysis of electrical and electronic circuits, chemical reaction simulations, optimization theory and automatic control, and many other areas. In this paper, the theory of normal forms of differential equations, originated in the works of Poincare and recently developed in the works of Arnold and his school, adapted to the simplest case of a degenerate differential equations. For this purpose we are using technique of Jordan chains, which was widely used in various problems of bifurcation theory. We study the normal forms of degenerate differential equations in the case of the existence of the maximal Jordan chain. Two and three dimensional spaces are studied in detail. Normal forms are the simplest representatives of the degenerate differential equations, which are equivalent to more complex ones. Therefore, normal forms should be considered as a model type of degenerate differential equations.
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Статья научная
The process of oil reservoir development in the elastic-water-drive mode is considered. It is assumed that the displacement of oil by the edge water occurs completely and a clear boundary between two liquids is formed in the reservoir, which moves according to a previously unknown law. Within the framework of a one-dimensional model of the elastic-water-drive development regime, the task is set to identify the main hydrodynamic parameters of the reservoir, i.e. the pressure at the interface between liquids, the pressure distribution in the reservoir and the position of the interface between liquids, only on the basis of information obtained from the gallery of production wells. The problem set belongs to the class of boundary inverse problems. By applying the methods of front straightening and difference approximation, the problem is reduced to solving a system of difference equations. A special representation is proposed to solve the system of difference equations, having previously written it down as a variational problem with local regularization. As a result, an explicit formula is obtained for determining the approximate value of the pressure at the interface of liquids and recurrent formulas for determining the distribution of pressure and the position of the interface of liquids in the reservoir at each time layer. Based on the proposed computational algorithm, numerical experiments were carried out for a model oil reservoir.
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Numerical Study of Swirling Jet Streams Based on Modern Turbulence Models
Статья научная
This article examines a swirling jet based on a two-fluid turbulence model. This task, despite its simplicity, is quite a difficult task for many turbulence models. Because anisotropic turbulence is observed in swirling flows. Therefore, many modern RANS models are not able to describe such flows even qualitatively. The two-fluid model used in this work has been developed recently. Pioneering work shows that the basis for constructing this model is the possibility of representing a turbulent flow as a heterogeneous mixture of two liquids. Approach was proposed by Spaulding. The idea of the approach is to represent turbulence as the interpenetrating motion of two fluids, with the pulsating nature of the turbulent flow being caused by the relative moverment of them. For each fluid, it's own equation of motion is written, which leads to a closed system of equations. These studies also show that the developed two-fluid model is able to adequately describe complex anisotropic turbulence. To numerically implement the equations of a turbulent axisymmetric swirling jet, a uniform staggered calculation grid and a control volume method were used, and velocity correction was carried out using a simple method. The numerical results obtained are compared with experimental data from the ERCOFTAC database. It is shown that the results of the two-fluid model, despite the use of a rather rough computational grid, are in satisfactory agreement with experimental data.
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Numerical algorithm and computational experiments for one linear stochastic Hoff model
Статья научная
Investigated is a model of deformation in a structure composed of I-beams with random external effect; it is based on stochastic Hoff equations with an initial-final condition. The article describes an algorithm for a numerical solution of the initial-final problem for stochastic Hoff equations; the algorithm is based on the Galerkin method. Provided is a numerical investigation algorithm providing for numerical solutions for both degenerate and non-degenerate equations. The main theoretical results that enabled this numerical investigation are the methods of the theory of degenerate groups of operators and of the theory of the Sobolev type equations. The algorithms are represented by schemes enabling building flowcharts of programs for computational experiments. Results of computational experiments. In addition, numerical investigation of the stochastic model involves further obtaining and processing the results of experiments at various values of a random variable, including those related to rare events.
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