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

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Grmela, M.; Gorban, A.N.; Горбань, Александр Николаевич; Карлин, Илья Вениаминович

[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 [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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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.

[Electronic resource]. - Электрон. дан. (91 Kb) : статья / A.N. Gorban, I.V. Karlin, H.C. Ottinger. - Электрон. дан. (91 Kb) // Xiv:cond-mat/0209319. - 2002
   Перевод заглавия: Аддитивные обобщения энтропии Больцмана

ГРНТИ

29.17

Аннотация: There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solution to the corresponding extension of the classical ensembles, and discuss in some detail the example of the deformation of the uncorrelated state.

http://icm.krasn.ru/refextra.php?id=2090,
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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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

[Electronic resource]. - Electronic data (118 Kb) : научное издание / A.N. Gorban, I.V. Karlin. - Electronic data (118 Kb) // arXiv:cond-mat/0205511. - 2002. - Vol.1
   Перевод заглавия: Семейство аддитивных функций энтропии за рамками термодинамического предела

ГРНТИ

29.17

Аннотация: Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description of certain effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from Tsallis entropies, and is essentially a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function introduced by Burg. An example of how longer tails are described within the present approach is worked out for the canonical ensemble. In addition, we discuss a possible origin of a hidden statistical dependence, and give explicit recipes how to construct corresponding generalizations of master equation.

http://icm.krasn.ru/refextra.php?id=2105,
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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, I.V. Karlin, H.C. Ottinger // Physical review E. - 2003. - Vol. 67, Iss. 6. - Ст. 067104, DOI 10.1103/PhysRevE.67.067104 . - ISSN 1539-3755

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

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

[Text] : статья / A.N. Gorban, I.V. Karlin // Physical review E. - 2003. - Vol. 67, Iss. 1. - Ст. 016104, DOI 10.1103/PhysRevE.67.016104 . - ISSN 1539-3755

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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 / R. A. Brownlee, A. N. Gorban, J. Levesley // Physica A. - 2008. - Vol. 387, Iss. 2-3. - p. 385-406DOI 10.1016/j.physa.2007.09.031 . -
Аннотация: We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity - nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy "trimming") and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimate of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid. All limiter constructions are applicable for both entropic and non-entropic quasiequilibria.

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

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Levesley, J.

[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] : статья / S. S. Chikatamarla, I. V. Karlin // Computer Physics Communications. - 2008. - Vol. 179, Iss. 1-3. - p. 140-143DOI 10.1016/j.cpc.2008.01.037 . -
Аннотация: Recently, a general theory of constructing lattice Boltzmann models as an approximation to the Boltzmann equation has been introduced [S. Chikatamarla, I. Karlin, Phys. Rev. Lett. 97 (2006) 190601]. We extend this theory to two dimensions and identify a new complete Galilean invariant lattice Boltzmann model. A general theory of constructing discrete velocity sets in higher dimensions is presented. Further implementation and optimization techniques are discussed.

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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 / A. N. Gorban, H. P. Sargsyan, H. A. Wahab // Mathematical Modelling of Natural Phenomena. - 2011. - Vol. 6, Iss. 5. - p. 184-262DOI 10.1051/mmnp/20116509 . -
Аннотация: Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell–jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.


Доп.точки доступа:
Sargsyan, H.P.; Wahab, H.A.; Горбань, Александр Николаевич

[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

[] / M. G. Sadovsky, I. Borovikov // J. Sib. Fed. Univ. Math. Phys. - 2014. - Vol. 7, Is. 1. - P112-123 . - ISSN 1997-1397
Аннотация: The paper presents a novel approach to statistical analysis of financial time series. The approach is based on n-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally continuous) financial data is considered: so called binary quantization. Possible applications of the proposed technique include market event study with the n-grams of higher information value. The finite length of the input data presents certain computational and theoretical challenges discussed in the paper. also, some other versions of a quantization are discussed. © Siberian Federal University. All rights reserved.

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РИНЦ

Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
Nekkar.Net Labs, Ltd, CA, United States

Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Borovikov, I.

/ A. N. Gorban, I. V. Karlin // Physica A: Statistical Mechanics and its Applications. - 1994. - Vol. 206, Is. 3-4. - P401-420 . - ISSN 0378-4371
Аннотация: The problem of thermodynamic parameterization of an arbitrary approximation of reduced description is solved. On the base of this solution a new class of model kinetic equations is constructed that gives a model extension of the chosen approximation to a kinetic model. Model equations describe two processes: rapid relaxation to the chosen approximation along the planes of rapid motions, and the slow motion caused by the chosen approximation. The H-theorem is proved for these models. It is shown, that the rapid process always leads to entropy growth, and also a neighborhood of the approximation is determined inside which the slow process satisfies the H-theorem. Kinetic models for Grad moment approximations and for the Tamm-Mott-Smith approximation are constructed explicitly. In particular, the problem of concordance of the ES-model with the H-theorem is solved. В© 1994.

Scopus

Держатели документа:
Nonequilibrium Systems Laboratory, Computing Center, Russian Academy of Sciences, 660 036 Krasnoyarsk -36, Russian Federation
ИВМ СО РАН

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

[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.

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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.

[Text] / I. V. Karlin, S. . Succi // Phys. Rev. E. - 1998. - Vol. 58, Is. 4. - PR4053-R4056, DOI 10.1103/PhysRevE.58.R4053. - Cited References: 6 . - ISSN 1063-651XРУБ Physics, Fluids & Plasmas + Physics, Mathematical

Аннотация: We develop a systematic method of constructing equilibria for kinetic models with discrete microscopic velocities. The approach is based on a suitable entropy maximum principle. The H theorem is demonstrated in the continuous and discrete space-time realizations. In addition, we discuss an extension of the Lattice Boltzmann method to irregular grids. [S1063-651X(98)50410-2].

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Держатели документа:
RAS, Ctr Comp, Krasnoyarsk 660036, Russia
Ist Applicaz Calcolo, I-00161 Rome, Italy
ИВМ СО РАН

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