Труды сотрудников ИВМ СО РАН

[Text] : статья / A.N. Gorban, I.V. Karlin, P. Ilg, H.C. Ottinger // Journal of Non-Newtonian Fluid Mechanics. - 2001. - Vol. 96, Iss. 1-2. - p. 203-219
Аннотация: We give a compact non-technical presentation of two basic principles for reducing the description of nonequilibrium systems based on the quasi-equilibrium approximation. These two principles are: construction of invariant manifolds for the dissipative microscopic dynamics, and coarse-graining for the entropy-conserving microscopic dynamics. Two new results are presented: first, an application of the invariance principle to hybridization of micro-macro integration schemes is introduced, and is illustrated with non-linear dumbbell models; second, Ehrenfest's coarse-graining is extended to general quasi-equilibrium approximations, which gives the simplest way to derive dissipative equations from the Liouville equation in the short memory approximation.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Ilg, P.; Ottinger, H.C.; Горбань, Александр Николаевич

[Text] : статья / I.L. Arshukova, N.V. Erkaev, H.K. Biernat // International journal of geomagnetism and aeronomy. - 2002. - Vol. 3, № 1. - p. 27–34
Аннотация: This article deals with the magnetohydrodynamic instability of the high magnetic shear magnetopause, which is considered to be a thin layer with a constant curvature radius and plasma velocity shear. In our model, the magnetic field and plasma density are assumed to be piecewise constant in three regions: in the magnetosphere adjacent to the magnetopause, in the magnetosheath, and inside a thin layer associated with the magnetopause. The plasma parameters and the magnetic field are assumed to obey the ideal incompressible magnetohydrodynamics. A Fourier analysis is used to calculate small perturbations of magnetic field and plasma parameters near the magnetopause in a linear approximation. The instability growth rate is obtained as a function of the angle between the velocity vector and the geomagnetic field direction for different plasma bulk speeds, wave numbers and curvature radii. The resulting instability is a mixture of interchange and Kelvin-Helmholtz instabilities on a surface with a nonzero curvature. The instability growth rate is an increasing function of the tangential velocity component perpendicular to the magnetic field. On the other hand, the growth rate is a decreasing function of the velocity component along the magnetic field.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Biernat, H.K.; Аршукова И.Л.

[Text] : статья / N.V. Erkaev [et al.] // International journal of geomagnetism and aeronomy. - 2002. - Vol. 3, № 1. - p. 67-76
Аннотация: One aspect of the Io-Jupiter interaction studied by many authors is the generation of Alfv_en waves by Io moving in the magnetized plasma. In our study, we focus on an additional mechanism of the interaction between Io and Jupiter based on MHD slow shocks propagating from Io toward Jupiter along a magnetic ux tube. These MHD slow shocks are produced by plasma ow injected by Io, which is considered as a source of ionized particles. The propagation of the slow shocks is calculated along a given magnetic ux tube from Io to Jupiter. The total pressure is assumed to be a known function of the distance measured along the tube. It is determined as the magnetic pressure corresponding to the undisturbed Jovian magnetic field calculated in a dipole approximation. The material coordinates are used to describe the plasma ow along the magnetic tube. The peculiarity of this problem stems from the fact that the total pressure increases by a factor of 105, whereas the cross section of the magnetic ux tube decreases by a factor of 300. The result is that the plasma velocity after the shock front substantially increases toward Jupiter with increasing magnetic pressure. The electric potential difference along the magnetic field is estimated, which is produced by the accelerated plasma ow propagating with the MHD slow shocks.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Semenov, V.S.; Семенов В. С.; Shaidurov, V.A.; Шайдуров В.А.; Langmayr, D.; Biernat, H.K.; Rucker, H.O.

[Text] : статья / N.V. Erkaev, V.A. Shaidurov, V.S. Semenov, H.K. Biernat // Nonlinear Processes in Geophysics. - 2002. - Vol. 9. - p. 163-172
Аннотация: Variations of the plasma pressure in a magnetic flux tube can produce MHD waves evolving into shocks. In the case of a low plasma beta, plasma pressure pulses in the magnetic flux tube generate MHD slow shocks propagating along the tube. For converging magnetic field lines, such as in a dipole magnetic field, the cross section of the mag-netic flux tube decreases enormously with increasing mag-netic field strength. In such a case, the propagation of MHD waves along magnetic flux tubes is rather different from that in the case of uniform magnetic fields. In this paper, the propagation of MHD slow shocks is studied numerically us-ing the ideal MHD equations in an approximation suitable for a thin magnetic flux tube with a low plasma beta. The results obtained in the numerical study show that the jumps in the plasma parameters at the MHD slow shock increase greatly while the shock is propagating in the narrowing mag-netic flux tube. The results are applied to the case of the interaction between Jupiter and its satellite Io, the latter be-ing considered as a source of plasma pressure pulses.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Shaidurov, V.A.; Шайдуров В.А.; Semenov, V.S.; Семенов В. С.; Biernat, H.K.; Еркаев, Николай Васильевич

[Text]. - Electronic data (106 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=1472. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/2000/1472erkaev_PHP03413_eng.pdf (Полный текст) : статья / Erkaev N.V., Biernat H.K., Farrugia C.J. - Electronic data (106 Kb) // Physics of Plasmas. - 2000. - Vol. 7, № 7. - p. 3413-3420

ГРНТИ

29.27.45

Аннотация: The plasma flow past a blunt obstacle in an ideal magnetohydrodynamic ~MHD! model is studied, taking into account the tensorial nature of the plasma pressure. Three different closure relations are explored and compared with one another. The first one is the adiabatic model proposed by Chew, Goldberger, and Low. The second closure is based on the mirror instability criterion, while the third depends on an empirical closure equation obtained from observations of solar wind flow past the Earth's magnetosphere. The latter is related with the criterion of the anisotropic ion cyclotron instability. In the presented model, the total pressure, defined as the sum of magnetic pressure and perpendicular plasma pressure, is assumed to be a known function of Cartesian coordinates. The calculation is based on the Newtonian approximation for the total pressure along the obstacle and on a quadratic behavior with distance from the obstacle along the normal direction. Profiles of magnetic field strength and plasma parameters are presented along the stagnation stream line between the shock and obstacle of an ideal plasma flow with anisotropy in thermal pressure and temperature.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Biernat, H.K.; Farrugia, C.J.; Еркаев, Николай Васильевич

[Text]. - Electronic data (249 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=788. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/788gorban_AMLappr98.pdf (Полный текст) : статья / A.N. Gorban. - Electronic data (249 Kb) // Applied Mathematics Letters. - 1998. - Vol. 11, № 3. - p. 45-49
   Перевод заглавия: Аппроксимация непрерывных функций нескольких переменных с помощью произвольной нелинейной непрерывной функции одного переменного, линейных функций и их суперпозиций
Аннотация: Linear spaces of continuous functions of real variables closed under the superposition operation are considered. It has been proved that when such a space contains constants, linear functions, and at least one nonlinear function, it is dense in the space of all continuous functions in the topology of uniform convergence on compact sets. So, the approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions is possible.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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Горбань, Александр Николаевич

[Text]. - Electronic data (45 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2110. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/2110gorban_PREMomMIM98.pdf (Полный текст) : статья / I.V. Karlin, A.N. Gorban, G. Dukek, T.F. Nonnenmacher. - Electronic data (45 Kb) // Physical review E. - 1998. - Vol. 57, № 2. - p. 1668-1672
   Перевод заглавия: Динамические поправки к моментным приближениям
Аннотация: Considering the Grad moment ansatz as a suitable first approximation to a closed finite-moment dynamics, the correction is derived from the Boltzmann equation. The correction consists of two parts, local and nonlocal. Locally corrected thirteen-moment equations are demonstrated to contain exact transport coefficients. Equations resulting from the nonlocal correction give a microscopic justification to some phenomenological theories of extended hydrodynamics

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Dukek, G.; Nonnenmacher, T.F.; Карлин, Илья Вениаминович

[Text] : статья / A.N. Gorban [et al.] // Physica A. - 1996. - 231. - p. 648-672
   Перевод заглавия: Траектории релаксации: глобальная аппроксимация
Аннотация: The paper intends to fill the gap of analytic approximate methods for non-linear space-independent dissipative systems equipped with the entropy functional. The key point of the analysis is an upper limiting state in the beginning of the relaxation. Extremal properties of this state are described and explicit estimations are derived. This limiting state is used to construct explicit approximations of the phase trajectories. Special attention is paid to accomplish positiv-ity, smoothness and the entropy growth along the approximate trajectories. The method is tested for the space-independent Boltzmann equation with various collisional mechanisms.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Karlin, I.V.; Карлин, Илья Вениаминович; Nonnenmacher, T.F.; Zmievskii, V.B.; Змиевский В.Б.

[Text] : статья / A.N. Gorban, V.I. Bykov, G.S. Yablonskii // Chemical Engineering Science. - 1986. - Vol. 41, № 11. - P2739-2745
   Перевод заглавия: Аналог термодинамических функций для реакций без взаимодействия различных веществ

ГРНТИ

31.15.25

Аннотация: Function similar to Lyapunov's function has been constructed for reactions with ?i Ai ?j ?j Aj stages. This provides for the quasi-thermodynamics of the appropriate kinetic model, which implies steady-state uniqueness and global stability in the reaction polyhedron. The kinetic law generalizing the Marcelin -de Donder kinetics has been written for a separate stage. Explicit Lyapunov thermodynamic functions have been written for various conditions of the reaction proceeding in closed systems. The matrix of linear approximation close to equilibrium is expressed by means of the introduced scalar product. Particularly, the absence of damped oscillations as equilibrium is approached as shown.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Bykov, V.I.; Быков, Валерий Иванович; Yablonskii, G.S.; Яблонский, Григорий Семенович; Горбань, Александр Николаевич

[Text] : статья / I.V. Karlin, A.N. Gorban // Annelen der Physik. - 2002. - Vol. 11, Iss. 10-11. - p. 783-833DOI 10.1002/1521-3889(200211)11:10/11783::AID-ANDP7833.0.CO;2-V
   Перевод заглавия: Гидродинамика из уравнений Грэда: чему мы можем научиться из точных решений?

ГРНТИ

29.17

Аннотация: A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description beyond the Navier-Stokes approximation. Various techniques, such as the method of partial summation, Pad_e approximants, and invariance principle are compared both in linear and nonlinear situations.

http://icm.krasn.ru/refextra.php?id=2103,
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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Карлин, Илья Вениаминович

[Текст] : статья / И.И. Рыжков // J. of Siberian Federal University. Mathematics & Physics. - 2010. - №3(4). - С. 433-449


Доп.точки доступа:
Gaponenko, Y.A.; Гапоненко, Юрий Анатольевич; Рыжков, Илья Игоревич

[Текст] : статья / E.A. Novikov // Computational Mathematics and Mathematical Physics . - 2011. - Vol. 51, № 12. - p. 2065-2078, DOI 10.1134/S0965542511120153 . - ISSN 0965-5425

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Новиков, Евгений Александрович

[Text] : статья / Chen H. и др. // Numerical Analysis and Applications. - 2011. - Vol. 4, Iss. 4. - p. 345-362DOI http://link.springer.com/article/10.1134%2FS1995423911040070 . -
Аннотация: In this paper, a modified method of characteristics in combination with integral identities of triangular and tetrahedral linear elements is used to prove a uniform optimal-order error estimate that depends only on the initial data and right-hand side, but not on a scaling parameter ɛ, for multidimensional time-dependent advection-diffusion equations.


Доп.точки доступа:
Chen, H.; Lin, Q.; Shaidurov, V.V.; Шайдуров, Владимир Викторович; Zhou, J.

[Text] : статья / V.V.Denisenko // Computational Research. - 2013. - Vol. 1, № 2. - p. 34 - 51DOI 10.13189/cr.2013.010203 . -
Аннотация: Conventional two dimensional model for electric fields in the Earth’s ionosphere is analyzed to estimate its error. The main difficulties arise due to asymmetry of the conductivity tensor. We use the energy method and small parameter expansion. To make it possible in spite of asymmetry of the tensor coefficients the problem is reduced to the problem of minimum of proper quadratic energy functional. The variational principle is stated and proved for the 3-D boundary value problem. The error of the 2-D approximation is analyzed in the case, when conductor occupies a flat layer 0 < z < z0 and is homogeneous in z direction, and the vector of magnetic field has only z component. The results of numerical simulation of the electric field penetration from ground to the Earth’s ionosphere with reduction of the 3-D model of the ionospheric conductor to the 2-D model are presented. Precision of such an approach is demonstrated.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Денисенко, Валерий Васильевич

/ A. Divin [et al.] // J. Geophys. Res-Space Phys. - 2012. - Vol. 117. - Ст. A06217, DOI 10.1029/2011JA017464. - Cited References: 43. - The present work is supported partially by the Onderzoekfonds KU Leuven (Research Fund KU Leuven), by the NASA MMS grant NNX08AO84G and by the European Commission's Seventh Framework Programme (FP7/2007-2013) under the grant agreement 263340 (SWIFF project, www. swiff. eu) and 269198 - Geoplasmas (Marie Curie International Research Staff Exchange Scheme). Additional support is provided by RFBR grants 09-05-91000-ANF-a, 12-05-00152-a and 12-05-00918-a, Austrian Science Fund project T193-N16 and by SPSU grants 11.38.47.2011 and 11.38.84.2012. The simulations were conducted on the resources of the Vlaams Supercomputer Centrum (VSC) at the Katholieke Universiteit Leuven. The authors wish to thank the reviewers for their comments that helped to improve the manuscript. . - ISSN 2169-9380РУБ Astronomy & Astrophysics

Аннотация: The Sweet-Parker analysis of the inner electron diffusion region of collisionless magnetic reconnection is presented. The study includes charged particles motion near the X-line and an appropriate approximation of the off-diagonal term for the electron pressure tensor. The obtained scaling shows that the width of the inner electron diffusion region is equal to the electron inertial length, and that electrons are accelerated up to the electron Alfven velocity in X-line direction. The estimated effective plasma conductivity is based on the electron gyrofrequency rather than the binary collision frequency, and gives the extreme (minimal) value of the plasma conductivity similar to Bohm diffusion. The scaling properties are verified by means of Particle-in-Cell simulations. An ad hoc parameter needs to be introduced to the scaling relations in order to better match the theory and simulations.


Доп.точки доступа:
Divin, A.; Lapenta, G.; Markidis, S.; Semenov, V.S.; Erkaev, N.V.; Еркаев, Николай Васильевич; Korovinskiy, D.B.; Biernat, H.K.

/ N.V. Erkaev, V.S. Semenov, H.K. Biernat // Phys. Plasmas. - 2012. - Vol. 19, Is. 6. - Ст. 62905, DOI 10.1063/1.4725506. - Cited References: 22. - This work is supported by RFBR Grants Nos. 12-05-00152-a and 12-05-00918-a, and also by St. Petersburg University grant. V. S. S. and H. K. B. are supported from the FP7 Programme under Grant No. 269198-Geoplasmas (Marie Curie Exchange Scheme). Additional support is due to the Austrian "Fonds zur Forderung der wissenschaftlichen Forschung" under Project I 193-N16 and the "Verwaltungsstelle fur Auslandsbeziehungen" of the Austrian Academy of Sciences. . - ISSN 1070-664XРУБ Physics, Fluids & Plasmas

Аннотация: Magnetic filament approach is applied for modeling of nonlinear "kink"-like flapping oscillations of thin magnetic flux tubes in the Earth's magnetotail current sheet. A discrete approximation for the magnetic flux tube was derived on a basis of the Hamiltonian formulation of the problem. The obtained system of ordinary differential equations was integrated by method of Rosenbrock, which is suitable for stiff equations. The two-dimensional exact Kan's solution of the Vlasov equations was used to set the background equilibrium conditions for magnetic field and plasma. Boundary conditions for the magnetic filament were found to be dependent on the ratio of the ionospheric conductivity and the Alfven conductivity of the magnetic tube. It was shown that an enhancement of this ratio leads to the corresponding increase of the frequency of the flapping oscillations. For some special case of boundary conditions, when the magnetic perturbations vanish at the boundaries, the calculated frequency of the "kink"-like flapping oscillations is rather close to that predicted by the "double gradient" analytical model. For others cases, the obtained frequency of the flapping oscillations is somewhat larger than that from the "double gradient" theory. The frequency of the nonlinear flapping oscillations was found to be a decreasing function of the amplitude. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4725506]


Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Semenov, V.S.; Biernat, H.K.

/ A.V. Lapko, V.A. Lapko // Optoelectronics, Instrumentation and Data Processing. - 2012. - Vol. 48, Is. 4. - pp. 416-422, DOI 10.3103/S8756699012040139 . - ISSN 8756-6990
Аннотация: Asymptotic properties of a nonparametric estimate of the separating surface equation defined in the space of independent attributes of classified objects are studied. Based on this analysis, the importance of the influence of a priori information about independence of random variables on the approximation properties of the nonparametric decision function in a two-alternative problem of pattern recognition is established. В© 2012 Allerton Press, Inc.

Scopus


Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

[Text] / I. O. Bogulskii, Y. M. Volchkov // Numerical Analysis and Applications. - 2012. - Vol. 5, Is. 2. - pp. 124-128, DOI 10.1134/S1995423912020048 . - ISSN 1995-4239
Аннотация: Numerical schemes for solving two-dimensional dynamic problems of elasticity theory based upon several local approximations for each of the required functions are discussed. The schemes contain free parameters (dissipation constants). An explicit form of artificial dissipation of the solutions allows us to control its size and to effectively construct both explicit and implicit schemes. The principle of producing such schemes is applied to a plane dynamic problem of elasticity theory as an example. We describe a class of problems for which numerical algorithms using several local approximations for each of the required functions are constructed. Examples of solving practical problems are given. В© 2012 Pleiades Publishing, Ltd.

Scopus,
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Доп.точки доступа:
Bogulskii, I.O.; Богульский, Игорь Олегович; Volchkov, Y.M.

[Text] / E. D. Karepova [et al.] // NUMERICAL ANALYSIS AND ITS APPLICATIONS. Ser. LECTURE NOTES IN COMPUTER SCIENCE : SPRINGER-VERLAG BERLIN, 2005. - Vol. 3401: 3rd International Conference on Numerical Analysis and Its Applications (JUN 29-JUL 03, 2004, Bousse, BULGARIA). - pp. 56-65. - Cited References: 4 . - ISBN 3-540-24937-0РУБ Computer Science, Interdisciplinary Applications + Computer Science, Theory & Methods + Mathematics, Applied

Аннотация: A boundary value problem for the Navier-Stokes equations for a viscous heat conducting gas in a finite computational domain is considered. The space approximation is constructed with the use of the Bubnov-Galerkin method combined with the method of lines.


Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Malyshev, A.V.; Малышев, Андрей Валерьевич; Shaidurov, V.V.; Шайдуров, Владимир Викторович; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Li, Z. \ed.\; Vulkov, L. \ed.\

[Text] / E. D. Karepova [et al.] // Computational Science and High Performance Computing II. Ser. NOTES ON NUMERICAL FLUID MECHANICS AND MULTIDISCIPLINARY DESIGN : SPRINGER-VERLAG BERLIN, 2006. - Vol. 91: 2nd Russian/Germany Advanced Research Workshop on Computational Science and High Performance Computing (MAR 14-16, 2005, Stuttgart, GERMANY). - pp. 41-54. - Cited References: 4 . - ISBN 3-540-31767-8РУБ Computer Science, Interdisciplinary Applications + Computer Science, Theory & Methods + Mathematics, Applied

Аннотация: A boundary value problem for the Navier-Stokes equations for a viscous heat conducting gas in a finite computational domain is considered. The space approximation is constructed with the use of the Bubnov-Galerkin method combined with the method of lines. The parallel realization of this method is discussed for multiprocessor computational system.


Доп.точки доступа:
Karepova, E.D.; Карепова, Евгения Дмитриевна; Malyshev, A.V.; Малышев, Андрей Валерьевич; Shaidurov, V.V.; Шайдуров, Владимир Викторович; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Krause, E \ed.\; Shokin, Y \ed.\; Resch, M \ed.\; Resch, \ed.\