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Sibirskii Zhurnal Industrial'noi Matematiki
2010, vol. 13, No 4 (44)
Contents
UDC 536.25
Gavrilov A. A., Minakov A. V., Dekterev A. A., Rudyak V. Ya.
A numerical algorithm for modeling laminary flows in an eccentric annular channelWe present a numerical algorithm for simulating the steady laminary flows of an incompressible fluid in annular channels with eccentricity and rotation of the interior cylinder. This algorithm enables us to describe this class of flows in a broad range of annular channels and flow parameters. We present the implementation and the results of testing our numerical methods in detail. For a series of flows in an annular clearance we compare the numerical results with the available analytic solutions and experimental data. In all cases considered the simulated data matches well the available experimental, analytic, and numerical solutions.
Keywords: annular channel, eccentricity, control volume method, SIMPLE-C algorithm, pressure gradient.
Pp. 3–14.Gavrilov Andrey Anatol'evich
Dekterev Aleksandr Anatol'evich
Minakov Andrey Viktorovich
Rudyak Valeriy Yakovlevich
Baker Hughes, Russian Research Center 4a Kutateladze str. 630090 Novosibirsk
Institute of Thermophysics SB RAS Siberian Federal University E-mail: gavand@yandex.ru; valery.rudyak@mail.ru
UDC 519.85:532.542
Epifanov S. P., Zorkal'tsev V. I.
The flow distribution problem in a nonclassical statementWe present the results of study of a nonclassical flow distribution problem, including the existence and uniqueness of its solution. Unlike in the classical flow distribution problem traditionally considered in the theory of hydraulic chains, the variables in the nonclassical problems can be the expenses of the medium being transported in or out at the separate nodes of the system and the pressure increments on some arcs. Meanwhile, in contrast to the classical flow distribution problem we may be given the pressure at some nodes, as well as the expenses and the loss of pressure on some arcs.
Keywords: flow distribution problem, system of equations, initial and dual optimization problems.
Pp. 15–24.Epifanov Sergey Petrovich
Zorkal'tsev Valeriy Ivanovich
Melentiev Institute of Energy Systems SB RAS. 130 Lermontova str.664033 Irkutsk. E-mail: epifanov\@isem.sei.irk.ru; zork@isem.sei.irk.ru
UDC 519.233
Kovalevskiy A. P., Kostin V. S., Khitsenko V. E.
Modeling and identification of a sequence of dependent random variables with a symmetric stable distributionWe model a stationary random sequence whose elements have a symmetric absolutely continuous stable distribution. The joint distribution of the elements of the sequence is determined by three parameters: the Hurst parameter, a stable law parameter, and a scale parameter. We justify and implement strongly consistent methods for estimating these parameters. We compare various methods for parameter estimation.
Pp. 25–37.Kovalevskiy Artem Pavlovich
Novosibirsk State Technical University. 20 Karl Marx prospekt. 630092 Novosibirsk
Novosibirsk State University. 2 Pirogova str. 630090 Novosibirsk
Kostin Vitaliy Sergeevich
Institute of Economics and Industrial Engineering SB RAS. 17 Lavrent'ev prospekt. 630090 Novosibirsk.
Khitsenko Vladimir Evgen'evich
Novosibirsk State Technical University. E-mail: pandorra@ngs.ru
UDC 517.965:514.74
Kyrov V. A.
Functional equations in pseudo-Euclidean geometryWe solve functional equations on the metrics of all phenomenologically symmetric geometries in dimension n + 1 that extend the metric of the n-dimensional pseudo-Euclidean geometry.
Keywords: functional equation, phenomenologically symmetric geometry.
Pp. 38–51.Kyrov Vladimir Aleksandrovich
Gorno-Altajsk State University. 14 Socialisticheskaya str. 649000 Gorno-Altajsk. E-mail: kfizika@gasu.ru
UDC 519.63:536.24
Lyubimova O. N., Pestov K. N., Gridasova E. A.
Mathematical modeling of the thermal process of diffusion welding of glass and metalWe analyze the specific features of the process of welding and deposition related to heat propagation in an intensely heated glass-metal composite. The knowledge of temperature fields is required for predicting deformations and stresses, the character of diffusion processes, and structural changes in the zone of thermal effects, as well as for refining the technological regime of welding. We propose a mathematical model which accounts for the associated character of thermal exchange in the system, the absoption of the latent melting heat in the phase transition, and the dependence of thermophysical properties of materials on temperature. We present the results of simulations graphically, making conclusions on their agreement with the previously published data and the efficiency of the proposed model and methods.
Pp. 52–63.Lyubimova Ol'ga Nikolaevna
Pestov Konstantin Nikolaevich
Gridasova Ekaterina Aleksandrovna
Far-Eastern State Technical University. 10a Pushkinskaya str. 690950 Vladivostok E-mail: berms@mail.ru
UDC 517.9
Neshchadim M. V.
Conservation laws for a system of diffusion reaction type with one spatial variableFor a system of diffusion reaction type equations with one spatial variable we find necessary and sufficient conditions allowing nontrivial first order conservation laws. We establish a theorem on a basis for conservation laws.
Keywords: diffusion reaction type systems, conservation laws.
Pp. 64–69.Neshchadim Mikhail Vladimirovich
Institute of Mathematics SB RAS. 4 Acad. Koptyug prospekt
Novosibirsk State University. 2 Pirogova str. 630090 Novosibirsk E-mail: neshch@math.nsc.ru
UDC 519.61:577.21
Nikolaev S. V., Zubairova U. S., Fadeev S. I., Mjolsness E., Kolchanov N. A.
A study of a one-dimensional model of the regulation of the size of recovery zone in biological tissue taking cell division into accountWe describe the modeling of the dynamics of the structure of the recovery zone in biological tissue in the formalism of parameterized L-systems on the example of the apical meristema of a plant germ. We consider the influence of the ratio of the characteristic times of cellular cycle and morphogen diffusion on the stability of spatially distributed molecular genetic control system. We show that cell division is a perturbing factor for the regulation system of the recovery zone structure. We determine conditions for the loss of stability of the regulation.
Keywords: mathematical modeling, dynamical systems with dynamical structure, parameterized L-systems, the apical meristema of a germ, cell division, molecular genetic control system.
Pp. 70–82.Nikolaev Sergey Vasil'evich
Zubairova Ul'yana Stanislavovna
Kolchanov Nikolay Aleksandrovich
Institute of Cytology and Genetics SB RAS. 10 Acad. Lavrent'ev prospekt
Fadeev Stanislav Ivanovich
Institute of Mathematics SB RAS. 4 Acad. Koptyug prospekt 630090 Novosibirsk
Eric Mjolsness
Department of Computer Science. University of California. Irvine, CA 92697-3435, USA. E-mail: nikolaev@bionet.nsc.ru
UDC 517.956
Pyatkov S. G.
On some inverse problems for elliptic equations and systemsWe study the inverse problems for determining the right-hand side of a special form and the solution for elliptic systems, including a series of elasticity systems. On the boundary of the region the solution satisfies either the Dirichlet conditions or the mixed Dirichlet–Neuman conditions. On a set of planes we allow the normal derivatives of the solution to have discontinuities of the first kind. The gluing conditions on the discontinuity surface are analogous to the continuity conditions for the displacement and stress fields for horizontally layered medium. The overdetermination conditions are integral (the average of the solution over some region is given) or local (the solution is specified on some lines). For these problems we study solvability conditions and the Fredholm property.
Keywords: elliptic system, elasticity theory, inverse problem, the Fredholm property.Pyatkov Sergey Grigor'evich
Yugra State University. 16 Chekhova str. 628012 Khanty-Mansiysk
Institute of Mathematics SB RAS. 4 Acad. Koptyug prospekt. 630090 Novosibirsk. E-mail: s_pyatkov@ugrasu.ru; pyatkov@math.nsc.ru
UDC 532.595:519.633
Rukavishnikov V. A., Tkachenko O. P.
An approximate solution to the nonlinear problem of underground pipeline deformationWe construct a geometrically nonlinear mathematical model of a pipeline as a shell in strongly viscous medium. We find a universal procedure for reducing the two-dimensional equations of motion to one-dimensional equations for long bent pipes. We construct a difference scheme and create a software bundle for analyzing the equations of this model numerically. Running simulations for particular cases of bent pipelines, we find deformations of the pipeline wall and calculate the displacement of its axis.
Keywords: curvilinear pipeline, finite deformation, difference scheme, simulations.
Pp. 97–109.Rukavishnikov Viktor Anatol'evich
Tkachenko Oleg Pavlovich
Computing Center FEB RAS. 65 Kim Yu Chen str.680000 Khabarovsk. E-mail: vark@mail.redcom.ru; tkacenko_oleg@rambler.ru
UDC 517.54
Salimov R. B., Shabalin P. L.
A generalization of the Schwarz–Christoffel formulaWe obtain a formula for mapping the upper half-plane conformally onto a polygonal region, generalizing the Schwarz–Christoffel formula to the case of a countable set of vertices. We indicate a connection of the construction of this mapping to the solution of the Hilbert boundary value problem with a countable set of discontinuity points of the coefficients and polynomial singularity of the index.
Keywords: the Schwarz–Christoffel formula, boundary conditions, index of the problem.
Pp. 109–117.Salimov Rasikh Bakhtigareevich
Shabalin Pavel Leonidovich
Kazan' State Architecture and Building University. 1 Zelenaya str. 420043 Kazan' E-mail: Pavel.Shabalin@mail.ru
UDC 517.929.4:517.977.54
Sedova N. O.
Sufficient conditions for stability and a construction of stabilizing controls for differential systems of a special form with delayWe present some sufficient conditions for global uniform and asymptotic stability, as well as algorithms for constructing stabilizing controls for %systems of a special form: triangular and chain integrators. The results, stated in terms of sign constant Lyapunov functions, hold for nonlinear nonautonomous systems. We illustrate the applications of these results by classical examples.
Pp. 118–130.Sedova Natal'ya Olegovna
Ul'yanovsk State University. 42 Tolstoy str. 432000 Ul'yanovsk. E-mail: sedovano@ulsu.ru
UDC 517.956
Chirkunov Yu. A.
Steady oscillations in a continuously inhomogeneous medium described by the Ovsyannikov equationUsing group analysis methods, for the Ovsyannikov equation with maximal symmetry which describes steady oscillations in a continuously inhomogeneous medium we obtain an exact solution to the boundary value problems for some regions (a generalized Poisson formula), which in particular can serve as test solutions for simulating steady oscillations in continuously inhomogeneous media. We find operators acting on the set of solutions in a one-parameter family of these equations.
Keywords: Ovsyannikov equation, maximal symmetry, steady oscillations in continuously inhomogeneous medium, intertwining operators, generalized Poisson formula.
Pp. 131–140.Chirkunov Yury Aleksandrovich
Novosibirsk State Technical University. 20 Karl Marx prospekt. 630092 Novosibirsk.
Institute of Computational Technologies SB RAS. 6 Lavrent'ev prospekt. 630090 Novosibirsk. E-mail: chr01@rambler.ru
UDC 519.24
Shiryaeva L. K.
Calculation of power measures of Grabbs' criterion for checking for one outlierWe obtain recurrences for calculating five measures of the David power of Grabbs' criterion in the case that a normally distributed sample contains an outlier. We show that the power measures are functions of the parameters of the outlier, the sample volume, and the critical values of the Grabbs statistics. We proved that all power measures, except for the fourth, are nonincreasing functions of the critical values of the Grabbs statistics, while the fourth power measure always has a local maximum. Using our formulas we ran model simulations of the power measures in the case of a normally distributed sample of 20 observations including one outlier. The results of the simulations turn out close to those expected theoretically.
Pp. 141–154.Shiryaeva Lyudmila Konstantinovna
Samara State Economics University. 141 Sovetskoj Armii str. 443090 Samara E-mail: Shiryeva_LK@mail.ru