Труды сотрудников ИВМ СО РАН

[Text] : статья / A.N. Gorban, I.V. Karlin, H.C. Ottinger, L.L. Tatarinova // Physical review E. - 2001. - Vol. 63. - Ст. 066124. - p. 1-6DOI 10.1103/PhysRevE.63.066124
   Перевод заглавия: Аргументация Эренфестов, расширенная до формализма неравновесной термодинамики

ГРНТИ

29.17

Аннотация: A general method of constructing dissipative equations is developed, following Ehrenfest's idea of coarse graining. The approach resolves the major issue of discrete time coarse graining versus continuous time macroscopic equations. Proof of the H theorem for macroscopic equations is given, several examples supporting the construction are presented, and generalizations are suggested.

http://icm.krasn.ru/refextra.php?id=2088,
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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; Ottinger, H.C.; Tatarinova, L.L.; Татаринова Л.Л.

[Electronic resource]. - Electronic data
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2102. - Электрон. версия печ. публикации : научное издание / Gorban A.N. Zinovyev A.Y. - Electronic data // Institut des Hautes Etudes Scientifiques Preprint. IHES M/01/36. - 2001
   Перевод заглавия: Визуализация данных с помощью метода упругих карт и его приложения в геномике, экономике и социологии
Аннотация: Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real biological, economical, sociological datasets and to some model data distributions.

http://icm.krasn.ru/refextra.php?id=2102


Доп.точки доступа:
Zinovyev, A.Y.; Зиновьев, Андрей Юрьевич; Горбань, Александр Николаевич

[Text] : статья / I.V. Karlin, M. Grmela, A.N. Gorban // Physical Review E. - 2002. - Vol. 65. - Ст. 036128. - p. 1-4DOI 10.1103/PhysRevE.65.036128
   Перевод заглавия: Двойственность в неэкстенсивной статистической механике
Аннотация: We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscopic observables.

http://icm.krasn.ru/refextra.php?id=2095,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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

[Text] : статья / A.N. Gorban, A. Rossiev, N. Makarenko, Y. Kuandykov, V. Dergachev // International Journal of Geomagnetism and Aeronomy. - 2002. - Vol. 3, № 2. - p. 191–197
Аннотация: A new method is presented to recover the lost data in geophysical time series. It is clear that gaps in data are a substantial problem in obtaining correct outcomes about phenomenon in time series processing. Moreover, using the data with irregular coarse steps results in the loss of prime information during analysis. We suggest an approach to solving these problems, that is based on the idea of modeling the data with the help of small-dimension manifolds, and it is implemented with the help of a neural network. We use this approach on real data and show its proper use for analyzing time series of cosmogenic isotopes. In addition, multifractal analysis was applied to the recovered 14C concentration in the Earth's atmosphere.

http://icm.krasn.ru/refextra.php?id=2790,
http://ijga.agu.org/v03/gai01384/gai01384.pdf,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Rossiev, A.; Россиев, Алексей Анатольевич; Makarenko, N.; Макаренко Н.; Kuandykov, Y.; Dergachev, V.; Горбань, Александр Николаевич

[Text]. - Electronic data (164 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=1496. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/2000/1496gorban_PhAPoly00.pdf (Полный текст) : статья / V.B. Zmievskii, I.V. Karlin, M. Deville. - Electronic data (164 Kb) // Physica A. - 2000. - 275. - p. 152-177
   Перевод заглавия: Универсальный предел в динамике разбавленных растворов полимеров
Аннотация: The method of invariant manifold is developed for a derivation of reduced description in kinetic equations of dilute polymeric solutions. It is demonstrated that this reduced description becomes universal in the limit of small Deborah and Weissenberg numbers, and it is represented by the (revised) Oldroyd 8 constants constitutive equation for the polymeric stress tensor. Coe_cients of this constitutive equation are expressed in terms of the microscopic parameters. A systematic procedure of corrections to the revised Oldroyd 8 constants equations is developed. Results are tested with simple flows.

http://icm.krasn.ru/refextra.php?id=1496,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Deville, M.; Змиевский В.Б.

[Text]. - Electronic data (133 Kb) : статья / A.N. Gorban, I.V. Karlin, V.B. Zmievskii, S.V. Dymova. - Electronic data (133 Kb) // Physica A. - 2000. - 275. - p. 361-379
   Перевод заглавия: Сокращение описания в химической кинетике
Аннотация: Models of complex reactions in thermodynamically isolated systems often demonstrate evolution towards low-dimensional manifolds in the phase space. For this class of models, we suggest a direct method to construct such manifolds, and thereby to reduce the effective dimension of the problem. The approach realizes the invariance principle of the reduced description, it is based on iterations rather than on a small parameter expansion, it leads to tractable linear problems, and is consistent with thermodynamic requirements. The approach is tested with a model of catalytic reaction.

http://icm.krasn.ru/refextra.php?id=2086,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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

[Text]. - Electronic data (107 Kb) : статья / I.V. Karlin, A.N. Gorban, S. Succi, V. Boffi. - Electronic data (107 Kb) // Physical review letters. - 1998. - Vol. 81. - p. 6-9
   Перевод заглавия: Принцип максимума энтропии для решеточных кинетических уравнений
Аннотация: The entropy maximum approach to constructing equilibria in lattice kinetic equations is revisited. For a suitable entropy function, we derive explicitly the hydrodynamic local equilibrium, prove the H theorem for lattice Bhatnagar-Gross-Krook models, and develop a systematic method to account for additional constraints.

http://icm.krasn.ru/refextra.php?id=2094.,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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

[Electronic resource]. - Electronic data (232 Kb) : статья / A.N. Gorban, Y.I. Shokin, V.I. Verbitskii. - Electronic data (232 Kb) // arXiv:physics/9702021 . - 1997
   Перевод заглавия: Совместно диссипативные операторы и инфинитиземальный эффект Мура в интервальных пространствах
Аннотация: In solving a system of ordinary differential equations by an interval method the approximate solution at any considered moment of time t represents a set (called interval) containing the exact solution at the moment t. The intervals determining the solution of a system are often expanded in the course of time irrespective of the method and step used. ??The phenomenon of interval expansion, called the Moore sweep effect, essentially decreases the efficiency of interval methods. In the present work the notions of the interval and the Moore effect are formalized and the Infinitesimal Moore Effect (IME) is studied for autonomous systems on positively invariant convex compact. With IME the intervals expand along any trajectory for any small step, and that means that when solving a system by a stepwise interval numerical method with any small step the interval expansion takes place for any initial data irrespective of the applied method. The local conditions of absence of IME in terms of Jacoby matrices field of the system are obtained. The relation between the absence of IME and simultaneous dissipativity of the Jacoby matrices is established, and some sufficient conditions of simultaneous dissipativity are obtained. (The family of linear operators is simultaneously dissipative, if there exists a norm relative to which all the operators are dissipative.)??

http://icm.krasn.ru/refextra.php?id=2093,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Shokin, Y.I.; Шокин, Юрий Иванович; Verbitskii, V.I.; Вербицкий В.И.; Горбань, Александр Николаевич

[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.

http://icm.krasn.ru/refextra.php?id=2092,
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Держатели документа:
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 / 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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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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

[Electronic resource] : научное издание / A.N. Gorban, I.V. Karlin // arXiv:cond-mat/0207231. - 2002. - Vol.1 : комбин.
   Перевод заглавия: Метод инвариантного многообразия в химической кинетике

ГРНТИ

29.17

Аннотация: In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A review of existing alternative methods is extended by a thermodynamically consistent version of the method of intrinsic low-dimensional manifolds. A grid-based version of MIM is developed, and model extensions of low-dimensional dynamics are described. Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reduce description in chemical kinetics.

http://icm.krasn.ru/refextra.php?id=2106


Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Горбань, Александр Николаевич

[Текст] : статья / Е.А. Новиков // J. of Applied and Industrial Mathematics. - 2010. - Vol.4, №.4. - С. 1-12


Доп.точки доступа:
Новиков, Евгений Александрович

[Text] : статья / E.A. Novikov, Yu.V. Shornikov, B.U. Uatay // Proceedings of the IASTED International Conference Modelling, Identification, and Control / MIC 2011. - 2011. - p. 28-33DOI 10.2316/P.2011.718-087 . -

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

Доп.точки доступа:
Shornikov, Yu.V.; Шорников Ю.В.; Uatay, B.U.; Уатай Б.У.; Новиков, Евгений Александрович; The IASTED International Conference on Modelling, Identification, and Control(February 14 - 16, 2011 ; Innsbruck)

[Text] : статья / Yu.I. Shokin, V.V. Moskvichev, V.V. Nicheporchuk // Vulnerability, Uncertainty, and Risk: Analysis, Modeling, and Management. Proceedings of The First International Conference on Vulnerability and Risk Analysis and Management (ICVRAM 2011) and The Fifth International Symposium on Uncertainty Modeling and Analysis (ISUMA 2011). - Reston : ASCE, 2011. - p. 442-449, DOI 10.1061/41170(400)54 . - ISBN 978-0-7844-1170-4

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

Доп.точки доступа:
Moskvichev, V.V.; Москвичев, Владимир Викторович; Nicheporchuk, V.V.; Ничепорчук, Валерий Васильевич; Шокин, Юрий Иванович; International Conference on Vulnerability and Risk Analysis and Management(I ; April 11-13, 2011 ; Hyattsville); International Symposium on Uncertainty Modeling and Analysis(V ; April 11-13, 2011 ; Hyattsville)

[Text] : статья / E. A. Novikov // Automation and Remote Control. - 2012. - Vol. 73, Iss. 1. - p. 191-197DOI 10.1134/S0005117912010183 . -
Аннотация: An L-stable (2,1)-method with second-order accuracy is developed for solving stiff nonautonomous problems. At each step, the right-hand side of the system, as well as Jacobian matrix decomposition are evaluated only once. Efficiency of the integration method is illustrated using ring modulator calculation as an example.

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Доп.точки доступа:
Новиков, Евгений Александрович

[Text] : статья / E. A. Novikov, G. V. Vashchenko // Int. J. of Applied and Fundamental Research. Physical and Mathematical Science . - 2011. - № 1. - p. 101-102

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Доп.точки доступа:
Vashchenko, G.V.; Новиков, Евгений Александрович

[Text] : статья / V.B. Bekezhanova // Journal of Applied Mechanics and Technical Physics. - 2011. - Vol. 52, Iss. 1. - p. 74-81DOI 10.1134/S0021894411010111 . -
Аннотация: An exact solution is obtained for the problem of steady flow in a system of two horizontal layers of immiscible fluids with a common interface. The stability of the flow is studied by a linearization method. It is shown that the occurrence of instabilities is due to the different governing parameters of the fluids (thickness, heating conditions, viscous and thermal conductivity of the fluids). It is found that under constant gravity conditions, the perturbations are monotonic, and in zero gravity, oscillatory thermocapillary instability occurs.

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Доп.точки доступа:
Бекежанова, Виктория Бахытовна

[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 // Siberian mathematical journal. - 2011. - Vol. 52, № 2. - p. 207-221DOI 10.1134/S0037446611020030 . -
Аннотация: We propose some minimum principle for an energy functional in an elliptic boundary value problem that arises in constructing time-harmonic solutions to the Maxwell equations. We suggest the potentials other than the vector and scalar potentials, used in the mathematical modeling of electromagnetic fields since the operators of traditional problems are not sign definite, which complicates constructions of iterative solution methods. We consider the problem in a parallelepiped whose boundary is ideally conducting. For nonresonant frequencies we prove that the operator of the boundary value problem is positive definite, propose a minimum principle for a quadratic energy functional, and prove the existence and uniqueness of generalized solutions.

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

Доп.точки доступа:
Денисенко, Валерий Васильевич

[Text] : статья / O.V. Kaptsov, A.V. Schmidt // Symmetry Integr.Geom. Methods Appl. - 2012. - Vol. 8. - Ст. 073DOI 10.3842/SIGMA.2012.073 . -

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

Доп.точки доступа:
Schmidt, A.V.; Шмидт, Алексей Владимирович; Капцов, Олег Викторович