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Sibirskii Zhurnal Industrial'noi Matematiki
2015, vol. 18, No 3 (63)Contents
UDC 519.676
DOI 10.17377/sibjim.2015.18.301Averina T. A., Artem'ev S. S., and Smirnov D. D.
Numerical analysis on a supercomputer of a stochastic model of a longitudinal motion of a missile by the Monte-Carlo methodWe consider a model of the longitudinal motion of a roll-stabilized missile defined by a stochastic system with random structure. For the numerical solution, we use a statistical algorithm. The analysis of the solution is carried out using a frequency characteristic that is a generalization of an integral curve. The results of numerical experiments implemented on the SAB-30T cluster at the Siberian Supercomputer Center at the ICMMG of SDRAS.
Keywords: system with random structure, stochastic differential equation, Monte-Carlo method, parallel algorithm, missile, frequency integral curve.
Pp. 3-10.
Averina Tatyana Alexandrovna
Artem'ev Sergei Semenovich
Institute of Computational Mathematics and Mathematical Geophysics SD RAS
6 Lavrent'ev av.
Novosibirsk State University
Smirnov Dmitrii Dmitrievich
Novosibirsk State University
2 Pirogova st.
630090 Novosibirsk
E-mail: ata@osmf.sscc.ru; ssa@osmf.sscc.ru; smirnovdd@mail.ru
UDC 517.98:519.677
DOI 10.17377/sibjim.2015.18.302Derevtsov E. Yu. and Maltseva S. V.
Reconstruction of the singular support of a tensor field given in a refractive medium from its ray transformWe propose some approaches to the numerical solution of the problem of reconstruction of the singular support of a symmetric tensor field from its ray transform. For solving the problem, we use the back-projection operators acting on the ray transforms and the method of tensor analysis for a Riemannian manifold. We construct the indicator operators of inhomogeneity of the medium making it possible to allocate the sets of points of the singular support of scalar, vector, and tensor fields. Some algorithms for solving the problem are proposed and realized.
Keywords: tomography, tensor field, function break, singular support, refraction, ray transform, back-projection operator, tensor analysis.
Pp. 11-25.
Derevtsov Evgenii Yur'evich
Maltseva Svetlana Vasil'evna
Sobolev Institute of Mathematics SD RAS
4 Koptyug av.
Novosibirsk State University
2 Pirogova st.
Lavrent'ev Institute of Hydrodynamics SD RAS
15 Lavrent'ev av.
630090 Novosibirsk
E-mail: dert@math.nsc.ru; sv_maltseva@mail.ru
UDC 517.9
DOI 10.17377/sibjim.2015.18.303Zhalnina A. A. and Kucher N. A.
On the well-posedness of an inhomogeneous boundary value problem for the equations of mixtures of viscous compressible fluidsWe consider an inhomogeneous boundary value problem for the equations of a mixture of compressible viscous fluids, modeling a steady flow around an obstacle. The statement of the problem presumes the possibility of varying the shape of the obstacle. The well-posedness of such a problem in the class of strong solutions is proved. The results of the paper can be used for analyzing the optimal shape of an obstacle in a flow of a mixture of compressible viscous fluids.
Keywords: boundary value problem, mixture of viscous compressible fluids, strong solution, flow around an obstacle.
Pp. 26-39.
Kucher Nikolai Alekseevich
Zhalnina Aleksandra Anatol'evna
Kemerovo State University
6 Krasnaya st.
650043 Kemerovo
E-mail: nakycher@rambler.ru; qwert1776@yandex.ru
UDC 539.374
DOI 10.17377/sibjim.2015.18.304Kovtanyuk L. V. and Rusanov M. M.
On the collision of an unloading wave with an advancing elastoplastic boundary in a flat heavy layerWe give the exact solution of the boundary value problem in the theory of large deformations of the collision of an unloading wave generated by the breakdown of a loaded elastoviscoplastic heavy layer from an inclined plane when overcoming the resistance caused by dry friction. The interaction is considered of such a discontinuity plane with elastoplastic boundary that continues moving towards it.
Keywords: elasticity, plasticity, viscosity, large deformation, dynamic problem, the unloading wave.
Pp. 40-48.
Kovtanyuk Larisa Valentinovna
Rusanov Maxim Mikhailovich
Institute of Automation and Control Processes FED RAS
5 Radio st.
690041 Vladivostok
E-mail: lk@iacp.dvo.ru; maxprimat@mail.ru
UDC 51-74
DOI 10.17377/sibjim.2015.18.305Levina A. B., Taranov S. V.
Construction of linear and robust codes based on the coefficients of the scaling functions of wavelet transformsWavelet transforms are used in many fields such as computer graphics, image and signal processing, and speech recognition. We propose a method for applying the wavelet transform in coding theory. Wavelet analysis is a special type of a linear transformation of the signals and physical data from which it is possible to construct a linear code. The schemes of error protection based on linear codes do not guarantee the same protection level against all possible errors but concentrate their detecting abilities on a certain set of errors. This dependence of the possibilities of a linear code of the error distribution can lead to a distortion in the protected data in the case when the error does not belong to the set of undetectable errors. To decrease the error masking probability, robust codes are used. The robust codes are nonlinear codes not depending on the type and dimension of the error. We propose methods for constructing linear and robust codes from wavelet transforms.
Keyword: robust code, linear code, wavelet decomposition, scaling function, error detecting probability.
Pp. 49-56.
Levina Alla Borisovna
Taranov Sergei Vladimirovich
ITMO University
49 Kronverskii av.
197101 St. Petersburg
E-mail: levina@cit.ifmo.ru; serg.tvc@mail.ru
UDC 681.5
DOI 10.17377/sibjim.2015.18.306Perepelkin E. A. and Poddubny V. I.
Modal control of mechanical systems by acceleration signalsA method is proposed for solving the problem of synthesis of output feedback for mechanical systems with measurable second derivatives of the generalized coordinates. The method is applied for solving the problem of the active suspension control of a car.
Keywords: mechanical system, modal control, car suspension.
Pp. 57-62.
Perepelkin Evgeny Alexandrovich
Poddubny Vladimir Ivanovich
Polzunov Altai State Technical University
46 Lenin av.
656038 Barnaul
E-mail: eap@list.ru
UDC 514.8:517.983:519.6
DOI 10.17377/sibjim.2015.18.307Polyakova A. P. and Svetov I. E.
Numerical solution of the problem of reconstruction of a potential vector field in a ball from its normal Radon transformWe propose a numerical solution of the problem of reconstruction of a potential vector field in a ball from the available values of the normal Radon transform. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations confirm that the method yields good results of reconstruction of potential vector fields.
Keywords: vector tomography, potential vector field, approximation, normal Radon transform, truncated singular value decomposition, orthogonal polynomials.
Pp. 63-75.
Polyakova Anna Petrovna
Svetov Ivan Evgen'evich
Sobolev Institute of Mathematics SB RAS
4 Koptyug av.
Novosibirsk State University
2 Pirogova st.
630090 Novosibirsk
E-mail: anna.polyakova@ngs.ru; svetovie@math.nsc.ru
UDC 517.958:532.582.92
DOI 10.17377/sibjim.2015.18.308Starovoitov V. N.
Steady solutions to the problem of the motion of a ball in a Stokes–Poiseuille flowThe existence is proved of steady solutions to the problem of motion of a rigid ball in a cylindrical pipe filled with a viscous incompressible fluid. The cross section of the pipe has an arbitrary form and the fluid flow is described by the Stokes equations. At infinity, the velocity profile tends to that of the Poiseuille flow. We show that a steady solution exists for any position of the ball in the pipe. The ball performs a rectilinear motion along the generatrices of the pipe and its linear and angular velocities depend on the position of the center of the ball in the cross-section of the cylinder.
Keywords: viscous incompressible fluid, rigid body, cylindrical pipe, steady motion.
Pp. 76-85.
Starovoitov Victor Nikolaevich
Lavrent'ev Institute of Hydrodynamics SD RAS
15 Lavrent'ev av.
Novosibirsk State University
2 Pirogova st.
630090 Novosibirsk
E-mail: starovoitov@hydro.nsc.ru
UDC 532.54
DOI 10.17377/sibjim.2015.18.309Filimonov S. A., Dekterev A. A., Sentyabov A. V., and Minakov A. V.
Simulation of conjugate heat transfer in a microchannel system by a hybrid methodWe propose some hybrid method for solving hydrodynamics and heat transfer problems in distributed hydraulic systems. The method is based on the fact that part of the elements of the model is presented in the form of network elements the solution of the flow distrbution problem in which is carried out basing on hydraulic network theory, and the flow on the remaining elements is calculated by space methods of computational hydrodynamics. We expose the results of testing the hybrid method in hydrodynamics and heat ransfer problems in microchannels.
Keywords: numerical modeling, computational hydrodynamics, hydraulic network theory, hybrid algorithm, microchannel, conjugate heat transfer.
E-mail: bdk@inbox.ru; dekterev@mail.ru; tov-andrey@ya.ru; sentyabov_a_v@mail.ru
Pp. 86-97.
Filimonov Sergei Anatol'evich
TORINS ltd
50/44, Akademgorodok
660036 Krasnoyarsk
Dekterev Aleksandr Anatol'evich
Minakov Andrei Viktorovich
Sentyabov Andrei Vasil'evich
Siberian Federal University
79 Svobodnyi av.
660041 Krasnoyarsk
Institute of Thermophysics SB RAS
1 Lavrent'ev av.
630090 Novosibirsk