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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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; Ottinger, H.C.; Tatarinova, L.L.; Татаринова Л.Л.

[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

[Electronic resource]. - Electronic data (640 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2109. - Электрон. версия печ. публикации . - Режим доступа: http://www.wkap.nl/prod/b/0-306-47401-8 : научное издание / A.N. Gorban, I.V. Karlin. - Electronic data (640 Kb) // Recent Developments in Mathematical and Experimental Physics, Volume C: Hydrodynamics and Dynamical Systems. - Dordrecht : Kluwer, 2002. - p. 19-43
   Перевод заглавия: Геометрия необратимости
Аннотация: A general geometrical setting of nonequilibrium thermodynamics is developed. The approach is based on the notion of the natural projection which generalizes Ehrenfests' coarse-graining. It is demonstrated how derivations of irreversible macroscopic dynamics from the microscopic theories can be addressed through a study of stability of quasiequilibrium manifolds.

http://icm.krasn.ru/refextra.php?id=2109,
http://www.wkap.nl/prod/b/0-306-47401-8


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

[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.

http://icm.krasn.ru/refextra.php?id=2098,
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Держатели документа:
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

/ N. V. Dmitriev, E. A. Dvurechenskaya // Meteorologiya i Gidrologiya. - 1994. - Is. 12. - P53-62 . - ISSN 0130-2906
Аннотация: Two mathematical models of admixture dispersion in a surface turbulent layer of the pool are considered. All hydrodynamic characteristics required for the models are determined using a thermodynamic model of the horizontally homogeneous upper turbulent layer of the ocean. Numerical experiments have been performed to estimate the influence of stratification on the admixture diffusion. The advantages and drawbacks of the models are discussed. The importance of consideration of the influence of stratification on admixture diffusion is shown.

Scopus

Держатели документа:
Vychislitel'nyj Tsentr SO RAN, Krasnoyarsk, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Dmitriev, N.V.; Dvurechenskaya, E.A.

/ A. N. Gorban [et al.]. - New York : Springer, 2006. - 282 p. - ISBN 038728575X. - ISBN 978-038728575-7 : Б. ц.
Аннотация: This book discusses mathematical models that are based on the concepts of classical equilibrium thermodynamics. They are intended for the analysis of possible results of diverse natural and production processes. Unlike the traditional models, these allow one to view the achievable set of partial equilibria with regards to constraints on kinetics, energy and mass exchange and to determine states of the studied systems of interest for the researcher. Application of the suggested models in chemical technology, energy and ecology is illustrated in the examples. © 2006 Springer Science+Business Media, LLC. All rights reserved.

Scopus

Держатели документа:
Department of Mathematics, Mathematical Modelling Centre, University of Leicester, Leicester LE1 7RH, United Kingdom
Institute of Computational Modelling, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
Energy Research Institute, Moscow, Russian Federation
Laboratory for Thermodynamics, Melentiev Energy Systems Institute, Irkutsk 664033, Russian Federation
Melentiev Energy Systems Institute, Irkutsk 664033, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Filippov, S.P.; Kaganovich, B.M.; Keiko, A.V.; Shamansky, V.A.; Shirkalin, I.A.
Свободных экз. нет

[Text] / V. M. Sadovskii, O. V. Sadovskaya ; ed. M. D. Todorov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES : AMER INST PHYSICS, 2015. - Vol. 1684: 7th International Conference on Application of Mathematics in Technical (JUN 28-JUL 03, 2015, Albena, BULGARIA). - Ст. UNSP 070006. - (AIP Conference Proceedings), DOI 10.1063/1.4934307. - Cited References:18 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: Based on the generalized rheological method, the mathematical model describing small deformations of a single-phase porous medium without regard to the effects of a fluid or gas in pores is constructed. The change in resistance of a material to the external mechanical impacts at the moment of pore collapse is taken into account by means of the von Mises-Schleicher strength condition. In order to consider irreversible deformations, alongside with the classical yield conditions by von Mises and Tresca-Saint-Venant, the special condition modeling the plastic loss of stability of a porous skeleton is used. The random nature of the pore size distribution is taken into account. It is shown that the proposed mathematical model satisfies the principles of thermodynamics of irreversible processes. Phenomenological parameters of the model are determined on the basis of the approximate calculation of the problem on quasi-static loading of a cubic periodicity cell with spherical voids. In the framework of the obtained model, the process of propagation of plane longitudinal waves of the compression in a homogenous porous medium, accompanied by the plastic deformation of a skeleton and the collapse of pores, is analyzed.

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Держатели документа:
SB RAS, Inst Computat Modeling, Akademgorodok 50-44, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.; Todorov, M.D. \ed.\

/ M. Varygina // Continuum Mech. Thermodyn. - 2018, DOI 10.1007/s00161-018-0725-8 . - Article in press. - ISSN 0935-1175
Аннотация: Mathematical models of micropolar plates and shells are considered within the framework of the approximation approach. The governing equations of the theories are written in a thermodynamically consistent form of the conservation laws. This ensures hyperbolicity and correctness of the initial boundary value problems. For numerical solution, we propose parallel algorithms for supercomputers with graphics processing units. The algorithms are based on the splitting method with respect to spatial variables. We present the results of numerical computations of wave propagation in micropolar rectangular plates and cylindrical panels for media with different types of microstructure particles. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

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Держатели документа:
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Varygina, M.

/ S. Kozlova [et al.] // Phys. Chem. Chem. Phys. - 2019. - Vol. 21, Is. 4. - P2140-2152, DOI 10.1039/c8cp06795c . - ISSN 1463-9076
Аннотация: Experimental data on Fick diffusion coefficients of ternary and higher mixtures depend on the reference frame; those which are in common use are associated with the average velocity either with respect to volume, mass or mole number. In this study, the dependence of diffusion coefficients on the reference frame is thoroughly analyzed for three ternary mixtures of different types. The first one, tetralin-isobutylbenzene-dodecane, can almost be considered as ideal, the second one, cyclohexane-toluene-methanol, exhibits liquid-liquid phase separation and the third one, water-ethanol-triethylene glycol, contains three associating species and is also strongly non-ideal. Experimental diffusion coefficient data sampled in the volume reference frame are transformed to the molar and mass reference frames. The required partial molar volumes are derived from present density measurements. Four additional mixtures are considered along a single or two composition paths. A highlight of this study is the existence of a strong similarity of the main diffusion coefficients in the volume and mass reference frames for all considered mixtures. When the excess volume is small, the coefficients in the molar reference frame are also similar. However, for the mixture with a large excess volume (containing water), the diffusion coefficients in the molar reference frame differ significantly, even indicating negative main diffusion coefficients. It is shown that negative main diffusion coefficients appear due to relatively large experimental uncertainties of cross diffusion coefficients, which are propagated and amplified by frame transformation. © 2019 the Owner Societies.

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Держатели документа:
Institute of Computational Modelling, SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Microgravity Research Center, Universite Libre de Bruxelles (ULB), CP-165/62, Av. F.D. Roosevelt 50, Brussels, B-1050, Belgium
Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, 660041, Russian Federation
Thermodynamics and Process Engineering, Technical University Berlin, Ernst-Reuter-Platz 1, Berlin, 10587, Germany

Доп.точки доступа:
Kozlova, S.; Mialdun, A.; Ryzhkov, I.; Janzen, T.; Vrabec, J.; Shevtsova, V.