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Sibirskii Zhurnal Industrial'noi Matematiki
2016, vol. 19, No 4 (68)Contents
UDC 519.622.2
DOI 10.17377/sibjim.2016.19.401
Aida-zade K. R., Ashrafova Y. R.
Calculation of a state of the system of discrete linear processes connected by nonseparated boundary conditionsWe propose some approach to solving a collection of linear discrete block-diagonal systems with boundary conditions not separated between the blocks.
Using the peculiarities of the structure of the system, we obtain formulas for the transfer of the values of the initial and final variables in the boundary conditions which is carried out in each of the blocks independently. The result is an algebraic system whose dimension is determined by the number of blocks and the unknowns are only those of the initial or final variables of each of the blocks. The results are given of the numerical solution of the problem which uses the finite-difference approximation method to the calculation of the transitional regimes of the motion of a fluid in pipelines of complex structure are given.Keywords: discrete system, decomposition, complex object, nonseparated condition, transfer of boundary conditions.
Pp. 3-14.
Aida-zade Kamil Rajab
Institute of Control Systems of NAS Azerbaijan
Institute of Mathematics and Mechanics of NAS Azerbaijan
Ashrafova Yegana Ramiz
Institute of Control Systems of NAS Azerbaijan
B. Vahabzade, 9
AZ1141 Baku
E-mail: kamil_aydazade@rambler.ru; ashrafova_yegana@yahoo.com
UDC 519.676
DOI 10.17377/sibjim.2016.19.402
Artemiev S. S., Ivanov A. A.
Analysis of the influence of random noises for self-oscillating chemical reactions by a Monte-Carlo method on supercomputersWe study the question of the influence of external and internal random noises on the behavior of the concentrations of the components
of chemical reactions and the use of statistical modeling for the solutions of the appearing stochastic differential equations. The results of numerical experiments are given. For the analysis of numerical solutions, we use frequency characteristics generalizing an integral curve and the phase portrait. The numerical experiments showed that even a random noise with low intensity causes all kinds of transitions from one oscillation mode to another in the solutions to the SDEs.Keywords: stochastic differential equation, cumulative frequency curve, frequency phase portrait, generalized Euler method, concentration, chemical reaction.
Pp. 15-21.
E-mail: ssa@osmf.sscc.ru; 6ppp@mail.ru
Artemiev Sergey Semenovich
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
ave. Acad. Lavrentyev, 6
Pirogova str., 2
Ivanov Aleksandr Aleksandrovich
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
630090 Novosibirsk
UDC 532.137:519.6
DOI 10.17377/sibjim.2016.19.403Galkin V. M., Bogoslovskii A. V., Volkov Yu. S.
Vibrational viscosimetry and a numerical method for finding the gelation dynamicsWe consider the equations describing the motion of the vibration sensor probe in a viscoelastic medium. A method for performing experiments and a data processing method for the simultaneous determination of the viscosity and the elasticity is proposed. Test calculations are carried out on a model example.
Keywords: gel-forming composition, viscosity, elasticity, mechanical resistance, interference, numerical method.
Pp. 22-30.
Galkin Vladislav M.
Tomsk State Polytechnic University
Lenin ave., 30
634050 Tomsk
Bogoslovskii Andrey V.
Institute of Petroleum Chemistry SB RAS
Akademichesky ave., 4
634021 Tomsk
Volkov Yuriy S.
Sobolev Institute of Mathematics SB RAS
Acad. Koptyug ave., 4
630090 Novosibirsk
E-mail: vlg@tpu.ru; volkov@math.nsc.ru; bav@ipc.tsc.ru
UDC 519.63
DOI 10.17377/sibjim.2016.19.404Karchevskii A. L.
Calculation of stresses in a coal seam in presence of gas diffusionsWe obtain the analitical expressions for computing stresses in a coal seam taking into account the diffusion of the gas. The solution is presented as a sum whose four terms are convergent series. All functions in the expressions can easily be computed either separately or successively; i.e, it is not required to solve infinite systems of equations.
Keywords: stress, plane problem of elasticity theory, biharmonic equation.
Pp. 31-43.
Karchevskii Andrey Leonidovich
Institute of Comprehensive Exploitation of Mineral Resources RAS
Kryukovsky deadlock, 4
111020 Moscow
E-mail: karchevs@math.nsc.ru
UDC 539.374
DOI 10.17377/sibjim.2016.19.405Kovtanyuk L. V., Panchenko G. L.
Creep and stress relaxation in the material of a cylindrical layer under it linear motionIn the framework of large deformation theory, we consider the defomation of a material with nonlinear elactic and viscous properties in the space between two rigid coaxial cylindrical surfaces when the internal surface moves rectilinearly. We study the uniformly accelerated motion of the internal cylinder, its subsequent motions at a constant speed, and the subsequent uniformly retarded motion to a stop. We calculate the stresses, the reversible and irreversible deformations, the displacements and study the stress relaxation after the complete stop of the cylinder.
Keywords: large deformations, creep, elasticity, viscosity, stress relaxation.
Pp. 44-50.
Kovtanyuk Larisa Valentinovna
Institute of Automation and Control Processes Far Eastern Branch of RAS
Radio str., 5
690041 Vladivostok
Panchenko Galina Leonidovna
Institute of Engineering and Metallurgy Far Eastern Branch of RAS
Metallurgov Street, 1
681005 Komsomolsk-on-Amur
Vladivostok State University of Economics and Service
Gogolya str., 41
690014 Vladivostok
E-mail: lk@iacp.dvo.ru, panchenko.21@yandex.ru
UDC 681.5.015
DOI 10.17377/sibjim.2016.19.406Lomov A. A.
On the asymptotic optimality of orthoregressional estimatesIt is shown that the orthoregressive (STLS) parameter estimates in simultaneous linear systems (including autonomous difference equations with matrix coefficients) converge to the maximum likelihood estimates and thus become asymptotically best in the limit case of large variances of random coordinates on the manifold of solutions to the system observed with additive random perturbations.
Keywords: linear autonomous difference equation, parameter identification, orthoregressive estimate, STLS estimate, asymptotic efficiency.
Pp. 51-60.
Lomov Andrey Aleksandrovich
Sobolev Institute of Mathematics SB RAS
Acad. Koptyug ave., 4
630090 Novosibirsk
Novosibirsk State University
Pirogova str., 2
630090 Novosibirsk
E-mail: lomov@math.nsc.ru
UDC 51-77:338.984
DOI 10.17377/sibjim.2016.19.407Mizyakin Y. K., Mizyakina V. A., Petrov N. A.
Mathematical modeling of economic indices for oil field developmentWe construct a mathematical model for the quantitative estimation of investment projects for developing oil fields at the stage of conceptual design. As the base of such a model we use the concept in which the field is considered as a cluster of single-type elements of an area well pattern. The model operates on the net present value as a continuous function of the process parameters and enables us to analyze a broad spectrum of possible options in implementing the investment project. Many important relations between the technical and economical parameters are obtained in a concise and practically suitable form through the application of operational calculus and the Laplace transform.
Keywords: oil field development strategy, net present value, Laplace transform.
Pp. 61-69.
Mizyakin Yury K.
Samara Design and Research Institute on Crude Oil Production
Vilonovskaya str., 18
443010 Samara
Mizyakina Vera A.
Samara State Aerospace University
Moskovskoe shosse, 34
443086 Samara
Petrov Nikolay A.
Samara Design and Research Institute on Crude Oil Production
E-mail: MizyakinYuK@samnipineft.ru; vera.mizyakina@gmail.com; PetrovNA@samnipineft.ru
UDC 621.316
DOI 10.17377/sibjim.2016.19.408Nekrasov S. A.
A method of calculating dynamical systems with lumped parameters, accounting for the error of input dataWe propose and justify a bilateral method for the calculation of dynamical systems with lumped parameters which takes into account the error of input data. We give a few examples demonstrating the efficiency of the method.
Keywords: interval method, bilateral method, error, guaranteed accuracy, dynamical system.
Pp. 70-80.
Nekrasov Sergey Alersandrovich
Platov South-Russian State Politechnical University
Prosveschenia str., 132
346428 Novocherkassk
E-mail: nekrasoff_novoch@mail.ru
UDC 519.634
DOI 10.17377/sibjim.2016.19.409Norkin M. V.
Formation of a cavity under an inclined separation impact of a circular cylinder under the free surface of a heavy fluidA dynamical mixed problem on an impact and the subsequent constant-speed motion of a circular cylinder in an ideal incompressible fluid. We study the influence of the physical and geometrical parameters of the problem on the form of the cavity and the configuration of the external free surface of the fluid at small times. We carry out an asymptotic analysis of the internal free boundary of the fluid which accounts for the dynamics of the separation points. The force of the reaction of the medium to the cylinder is found. The necessity of introducing additional cavitation zones for the dynamical impact problem is justified.
Keywords: ideal incompressible fluid, circular cylinder, blow with separation, free border, cavity, small times, Froude number, cavitation number.
Pp. 81-92.
E-mail: norkinmi@mail.ru
Norkin Michail Viktorovich
Southern Federal University
Department of Mathematics, Mechanics and Computer Science
Milchakov str., 8a
344090 Rostov-on-Don
UDC 517.95
DOI 10.17377/sibjim.2016.19.410Pyatkov S. G., Uvarova M. V.
On determining the source function in heat and mass transfer problems under integral overdetermination conditionsWe examine an inverse problem of determining the right-hand side (source function) in a parabolic equation from integral overdetermination
data. By a solution to a parabolic equation we mean a weak solution, and the right-hand side in this equation can be a distribution of a certain class. Under some conditions on the data of the problem, we demonstrate that this inverse problem is well-posed and, in particular, stability estimates hold.Keywords: inverse problem, second-order parabolic equation, boundary value problem, integral overdetermination condition, weak solution.
Pp. 93-100.
E-mail: s_pyatkov@ugrasu.ru; m_uvarova@ugrasu.ru
Pyatkov Sergey Grigor'evich
Yugra State University
Chekhova str., 16
628012 Khanty-Mansyisk
Sobolev Institute of Mathematics SB RAS
Acad. Koptyuga ave., 4
630090 Novosibirsk
Uvarova Matrena Vladimirovna
Yugra State University