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.

http://icm.krasn.ru/refextra.php?id=1808,
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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]. - 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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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

[Text] : alternative Grad equations / A.N. Gorban, I.V. Karlin // Physical Review E. - 1996. - Vol. 54, № 4. - p. R3109-R3112
   Перевод заглавия: Скорости рассеяния вместо моментов. Альтернативные уравнения Грэда
Аннотация: Scattering rates moments of collision integral! are treated as independent variables, and as an alternative to moments of the distribution function, to describe the rarefied gas near local equilibrium. A version of the entropy maximum principle is used to derive the Grad-like description in terms of a finite number of scattering rates. The equations are compared to the Grad moment system in the heat nonconductive case. Estimations for hard spheres demonstrate, in particular, some 10% excess of the viscosity coefficient resulting from the scattering rate description, as compared to the Grad moment estimation.

http://icm.krasn.ru/refextra.php?id=69,
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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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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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

/ D.B. Korovinskiy [et al.] // J. Geophys. Res-Space Phys. - 2013. - Vol. 118, Is. 3. - P1146-1158, DOI 10.1002/jgra.50206. - Cited References: 39. - This work is supported by the Austrian Science Fund (FWF): I193-N16, by the Onderzoekfonds KU Leuven (Research Fund KU Leuven), by RFBR Grants 12-05-00918-a and 12-05-00152-a, and by SPSU Grants 11.38.47.2011 and 11.38.84.2012. The research has received funding also from the European Union Seventh Framework Programme [FP7/2007-2013] under grant agreement 269198-Geoplasmas (Marie Curie International Research Staff Exchange Scheme) and 218816 (SOTERIA project). The simulations were conducted on the resources of the Vlaams Supercomputer Centrum (VSC) at the Katholieke Universiteit Leuven. N.V.E., V.S.S. and D.B.K. thank also ISSI for hospitality and financial support. The authors thank reviewers for their comments, which gave us the substantial aid in preparing of this manuscript. . - 13. - ISSN 2169-9380РУБ Astronomy & Astrophysics

Аннотация: The paper presents the detailed numerical investigation of the "double-gradient mode," which is believed to be responsible for the magnetotail flapping oscillations-the fast vertical (normal to the layer) oscillations of the Earth's magnetotail plasma sheet with a quasiperiod similar to 100-200 s. The instability is studied using the magnetotail near-equilibrium configuration. For the first time, linear three-dimensional numerical analysis is complemented with full 3-D MHD simulations. It is known that the "double-gradient mode" has unstable solutions in the region of the tailward growth of the magnetic field component, normal to the current sheet. The unstable kink branch of the mode is the focus of our study. Linear MHD code results agree with the theory, and the growth rate is found to be close to the peak value, provided by the analytical estimates. Full 3-D simulations are initialized with the numerically relaxed magnetotail equilibrium, similar to the linear code initial condition. The calculations show that current layer with tailward gradient of the normal component of the magnetic field is unstable to wavelengths longer than the curvature radius of the field line. The segment of the current sheet with the earthward gradient of the normal component makes some stabilizing effect (the same effect is registered in the linearized MHD simulations) due to the minimum of the total pressure localized in the center of the sheet. The overall growth rate is close to the theoretical double-gradient estimate averaged over the computational domain.

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

/ E. N. Vasil'ev // Tech. Phys. - 2012. - Vol. 57, Is. 12. - pp. 1656-1660, DOI 10.1134/S1063784212120286. - Cited References: 7 . - 5. - ISSN 1063-7842РУБ Physics, Applied

Аннотация: The temperature and specific and integrated powers of energy mechanisms of a stationary equilibrium arc discharge in a cylindrical channel in air under pressures of 0.1 and 1 MPa are determined from the solution to the Elenbaas-Heller equation for various values of current I and radius R. The results of computations are given in the form of diagrams of state intended for estimating the basic energy characteristics of electric arcs for the given values of I and R.




Доп.точки доступа:
Васильев, Евгений Николаевич

/ 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.

[Text] / E.N. Vasiliev // Thermophys. Aeromechanics. - 2010. - Vol. 17, Is. 3. - pp. 411-418, DOI 10.1134/S0869864310030121. - Cited References: 13 . - ISSN 0869-8643РУБ Thermodynamics + Mechanics

Аннотация: The modeling of the formation of the equilibrium arc discharge structure in the axisymmetric formulation was carried out in a wide range of the values of current and radius. The boundary separating the radiation and heat-conducting regimes of discharge combustion was determined from computed data. The influence of energy mechanisms on the structure of the discharge was analysed, and a channel model was proposed for computing its parameters in the radiation regime.


Доп.точки доступа:
Vasiliev, E.N.; Васильев, Евгений Николаевич

[Text] / E. N. Vasil'ev // Tech. Phys. - 2013. - Vol. 58, Is. 10. - P1420-1425, DOI 10.1134/S1063784213100277. - Cited References: 6 . - ISSN 1063-7842РУБ Physics, Applied

Аннотация: The temperature as well as specific and integrated powers of energy mechanisms for sustaining a steady equilibrium arc discharge in a cylindrical channel in argon and carbon dioxide under atmospheric pressure are determined by solving the Elenbaas-Heller equation for various values of current I and radius R. The results of computations are represented in the form of state diagrams intended for estimating the main energy parameters of electric arcs for preset values of I and R. For carbon dioxide, the effect of screening of the heat conduction mechanism at the discharge boundary, which is due to a peculiar temperature dependence of radiation properties, is detected.

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Доп.точки доступа:
Vasil'ev, E. N.; Васильев, Евгений Николаевич

[Text] : статья / V. K. Andreev, V. B. Bekezhanova // Fluid Dynamics. - 2008. - Vol. 43, № 2. - p. 176-184


Доп.точки доступа:
Bekezhanova, V.B.; Бекежанова, Виктория Бахытовна; Андреев, Виктор Константинович

[Text] : статья / E. Chiavazzo, I. V. Karlin // Journal of Computational Physics. - 2008. - Vol. 227, Iss. 11. - p. 5535–5560DOI 10.1016/j.jcp.2008.02.006 . -
Аннотация: The method of invariant grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992; A.N. Gorban, I.V. Karlin, A.Y. Zinovyev, Invariant grids for reaction kinetics, Physica A 333 (2004) 106–154; A.N. Gorban, I.V. Karlin, Invariant Manifolds for Physical and Chemical Kinetics, Lecture Notes Physics 660, Springer, Berlin Heidelberg, 2005, doi: 10.1007/b98103]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold: the invariant grid. A convenient way to get a first approximation of the SIM is given by the spectral quasi-equilibrium manifold (SQEM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992]. In the present paper, a flexible numerical method to construct the discrete analog of a quasi-equilibrium manifold, in any dimension, is presented. That object is named quasi-equilibrium grid (QEG), while the procedure quasi-equilibrium grid algorithm (QEGA). Extensions of the QEM notion are also suggested. The QEGA is a numerical tool which can be used to find a grid-based approximation for the locus of minima of a convex function under some linear constraints. The method is validated by construction of one and two-dimensional grids for a model of hydrogen oxidation reaction.

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

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

[Text] : статья / E. Chiavazzo [et al.] // Proceedings of the Combustion Institute. - 2008. - Vol. 32, Iss. 1. - p. 519–526DOI 10.1016/j.proci.2008.05.014 . -
Аннотация: The Method of Invariant Grid (MIG) is a model reduction technique based on the concept of slow invariant manifold (SIM). The MIG approximates the SIM by a set of nodes in the concentration space (invariant grid). In the present work, the MIG is applied to a realistic combustion system: an adiabatic constant volume reactor with H2–air at stoichiometric proportions. By considering the thermodynamic Lyapunov function of the detailed kinetic system, the notion of the quasi-equilibrium manifold (QEM) is adopted as an initial approximation to the SIM. One- and two-dimensional discrete approximations of the QEM (quasi-equilibrium grids) are constructed and refined via MIG to obtain the corresponding invariant grids. The invariant grids are tabulated and used to integrate the reduced system. Excellent agreement between the reduced and detailed kinetics is demonstrated.

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

Доп.точки доступа:
Chiavazzo, Eliodoro; Karlin, I.V.; Карлин, Илья Вениаминович; Frouzakisa, Christos; Boulouchos, Konstantinos

[Text] / D. Langmayr, H. K. Biernat, N. V. Erkaev // Phys. Plasmas. - 2005. - Vol. 12, Is. 10. - Ст. 102103, DOI 10.1063/1.2065370. - Cited References: 30 . - ISSN 1070-664XРУБ Physics, Fluids & Plasmas

Аннотация: This paper is the first approach for analyzing the influence of kappa-distributed particles on the modified two-stream instability (MTSI). It is assumed that the plasma consists of a magnetized Maxwellian electron contribution and unmagnetized kappa-distributed ions drifting across the electrons. Within an electrostatic approximation, the influence of the kappa parameter on the maximum growth rate of the MTSI is evaluated for the special case of parallel drift velocity and wave propagation.


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

[Text] : статья / Y. Gaponenko, S. Glockner, A. Mialdun, V. Shevtsova // Acta Astronautica. - 2011. - Vol. 69, Iss. 3-4. - p. 119-126DOI 10.1016/j.actaastro.2011.03.012 . -
Аннотация: We report on numerical and experimental study of two-phase flows in a tall annulus. The geometry corresponds to a cylindrical liquid column co-axially placed into an outer cylinder with solid walls. The internal column consists of solid supports at the bottom and top, while the central part is a liquid zone filled with viscous liquid and kept in its position by surface tension. Gas enters into the annular duct and entrains initially quiescent liquid. The liquid bridge interface is deformed by gravity and by a co-axial gas flow which is co- and counter directed with respect to gravity. A new experimental set-up including an optical system for precise measurements of the interface displacement has been designed and developed. In the experiments silicone oil 5cSt was used as a test liquid and air as gas. On numerical side the dynamical response of an isothermal liquid bridge to a coaxial gas flow is examined by simulations of the Navier–Stokes equations. The attention is focused on the following points: time-dependent formation of the equilibrium shape of a liquid bridge in gravity conditions and its deformation by a gas flow, simulation of a flow pattern in a liquid/gas system with deformed free surface. The comparison of the numerical and experimental results for the interface deformation exhibits a satisfactory agreement.

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Доп.точки доступа:
Glockner, S.; Mialdun, A.; Shevtsova, V.; Гапоненко, Юрий Анатольевич

[Text] : статья / A. N. Gorban, M. Shahzad // Entropy. - 2011. - Vol. 13, Iss. 5. - p. 966-1019DOI 10.3390/e13050966 . -
Аннотация: We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

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Доп.точки доступа:
Shahzad, Muhammad; Горбань, Александр Николаевич

[Text] : статья / A. N. Gorban, G. S. Yablonskii // Chemical Engineering Science. - 2011. - Vol. 66, Iss. 21. - p. 5388-5399DOI 10.1016/j.ces.2011.07.054 . -
Аннотация: The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions, etc.), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We prove two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions. Physically, this means that the irreversible reactions cannot be included in oriented cyclic pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.

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Доп.точки доступа:
Yablonskii, G.S.; Горбань, Александр Николаевич

[Text] : статья / G. S. Yablonsky [et al.] // EPL. - 2011. - Vol. 93, № 2. - Ст. 20004DOI 10.1209/0295-5075/93/20004 . -
Аннотация: We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, ẋ=Kx , the kinetic operator K is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, exp(Kt), is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the i-th pure state and measure the probability pj(t) of the j-th state (j≠i), and, similarly, measure pi(t) for the process, which starts at the j-th pure state, then the ratio of these two probabilities pj(t)/pi(t) is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.

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Доп.точки доступа:
Yablonsky, G.S.; Gorban, A.N.; Горбань, Александр Николаевич; Constales, D.; Galvita, V.V.; Marin, G.B.

[Текст] / V. I. BYKOV, A. S. MIKHAILOV, I. V. UPOROV // Zhurnal Fiz. Khimii. - 1981. - Vol. 55, Is. 2. - С. 505-507. - Cited References: 5 . - ISSN 0044-4537РУБ Chemistry, Physical


WOS

Держатели документа:
ACAD SCI USSR,CTR COMP,KRASNOYARSK,USSR
ИВМ СО РАН
Доп.точки доступа:
BYKOV, V.I.; Быков, Валерий Иванович; MIKHAILOV, A.S.; UPOROV, I.V.

[Text] / G. . Dukek, I. V. Karlin, T. F. Nonnenmacher // Physica A. - 1997. - Vol. 239, Is. 4. - P493-508, DOI 10.1016/S0378-4371(97)00015-0. - Cited References: 15 . - ISSN 0378-4371РУБ Physics, Multidisciplinary

Аннотация: A generalization of the previously introduced dissipative bracket formulation of dissipative kinetic equations is performed. This generalization offers an opportunity to write model equations in concordance with the entropy requirements in situations where one attempts to consider the dissipative dynamics near highly non-equilibrium states, A list of sufficient conditions generalizing both the detailed balance and the Stueckelberg unitarity condition is established for the relevant kinetic equations to have an analog of the Boltzmann H-theorem. Several specific patterns of an explicit derivation of the model kinetic equations are discussed, including the relaxation in a given initial direction, the relaxation between two non-equilibrium states, and the slow decay to the equilibrium.

WOS

Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK 660036,RUSSIA
ИВМ СО РАН

Доп.точки доступа:
Dukek, G.; Karlin, I.V.; Карлин, Илья Вениаминович; Nonnenmacher, T.F.

/ G. Dukek, I. V. Karlin, T. F. Nonnenmacher // Physica A: Statistical Mechanics and its Applications. - 1997. - Vol. 239, Is. 4. - P493-508 . - ISSN 0378-4371
Аннотация: A generalization of the previously introduced dissipative bracket formulation of dissipative kinetic equations is performed. This generalization offers an opportunity to write model equations in concordance with the entropy requirements in situations where one attempts to consider the dissipative dynamics near highly non-equilibrium states. A list of sufficient conditions generalizing both the detailed balance and the Stueckelberg unitarity condition is established for the relevant kinetic equations to have an analog of the Boltzmann H-theorem. Several specific patterns of an explicit derivation of the model kinetic equations are discussed, including the relaxation in a given initial direction, the relaxation between two non-equilibrium states, and the slow decay to the equilibrium.

Scopus

Держатели документа:
Department of Mathematical Physics, University of Ulm, Ulm D-89069, Germany
Computing Center, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Dukek, G.; Karlin, I.V.; Карлин, Илья Вениаминович; Nonnenmacher, T.F.