Труды сотрудников ИВМ СО РАН

[Electronic resource]. - Electronic data (210 Kb) : научное издание / Gorban A.N. Karlin I.V. . - Electronic data (210 Kb) // Contribution to the"Encyclopedia of Life Support Systems". - Oxford : EOLSS Publishers, 2001
   Перевод заглавия: Методы нелинейной кинетики
Аннотация: Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research

http://icm.krasn.ru/refextra.php?id=2108


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

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

[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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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] : 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

[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

[Text] : статья / S.V. Karpov, I.L. Isaev [и др.] // Colloid Journal. - 2009. - Vol. 71, № 3. - p. 340–344, 10.1134/S1061933X09030077 . - ISSN 1061-933X

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

Доп.точки доступа:
Isaev, I.L.; Gavrilyuk, A.P.; Гаврилюк, Анатолий Петрович; Gerasimov, V.S.; Grachev, A.S.

[Text] : статья / I.V. Krasnov, S.P. Polyutov // Russian Physics Journal. - 2004. - Vol. 47, № 4. - p. 461-467

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

Доп.точки доступа:
Polyutov, S.P.; Краснов, Игорь Васильевич

[Text] : статья / A.N. Gorban, I.V. Karlin // Chemical Engineering Science. - 2003. - Vol. 58, Iss. 21. - P4751-4768, DOI 10.1016/j.ces.2002.12.001 . - ISSN 0009-2509

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

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

[Текст] : статья / A.E. Novikov, E.A. Novikov // Вестник СибГАУ. - 2009. - Вып. 5(26). - С. 17-20
Аннотация: An algorithm of right-hand side and Jacobian formation of differential equations of chemical kinetics is described. Numerical simulation of the cesium cycle in the upper atmosphere is conducted by means of the L-stable method of the second order of accuracy with the control accuracy. The results of the computation are presented.

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Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович

[Text] : статья / I.V. Krasnov // Laser Physics. - 1994. - Vol. 4, № 5. - p. 906-921

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

Доп.точки доступа:
Краснов, Игорь Васильевич

/ N. N. Lukzen [et al.] // Dokl. Phys. Chem. - 2013. - Vol. 449. - P44-47, DOI 10.1134/S0012501613030056. - Cited References: 15. - This work was supported by the Russian Foundation for Basic Research (project nos. 11-03-00356 and 11-03-00296), the Siberian Branch of the RAS (interdisciplinary project no. 71), the Division of Chemistry and Materials Science, RAS (project no. 5.1.1), and program P-220 of the Government of the Russian Federation (grant no. 11.G34.31.0045). . - 4. - ISSN 0012-5016РУБ Chemistry, Physical


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Доп.точки доступа:
Lukzen, N.N.; Ivanov, K.L.; Sadovsky, V.M.; Садовский, Владимир Михайлович; Kaptein, R.; Sagdeev, R.Z.

/ S.V. Karpov, P.N. Semina, A.P. Gavrilyuk // Colloid J. - 2012. - Vol. 74, Is. 3. - pp. 305-312, DOI 10.1134/S1061933X12030052. - Cited References: 16. - Authors are thankful to G. A. Chiganova for discussions and helpful comments. Studies were carried out with the support of grants: the Presidium of RAS No 29 and No 31, OFN RAS III.9.5, IP SB RAS No 43, IP SB RAS (and SFU) No 101. . - ISSN 1061-933XРУБ Chemistry, Physical

Аннотация: The energy of pair interactions between metal nanoparticles of different sizes is shown to be able to increase upon coagulation due to the additional electrostatic effect resulting from mutual heteropolar charging of the particles. The tunnel electron transfer occurring upon the collisions between particles of different sizes may be the reason for the charging. The transfer is caused by the dependence of the electron work function on the particle size. The electron transfer through the interparticle gap equalizes the Fermi levels in particles of different sizes and is associated with this dependence. Using the example of bimodal silver nanocolloids, it is shown that mutual heteropolar charging of particles with different sizes may accelerate the coagulation of polydisperse colloidal systems by an order of magnitude or more as compared with monodisperse systems, in which this effect is absent.

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Karpov, S.V.; Semina, P.N.; Gavrilyuk, A.P.; Гаврилюк, Анатолий Петрович

[Text] / N.I. Kosarev, N.Y. Shaparev // Quantum Electron. - 2006. - Vol. 36, Is. 4. - pp. 369-375, DOI 10.1070/QE2006v036n04ABEH013153. - Cited References: 23 . - ISSN 1063-7818РУБ Engineering, Electrical & Electronic + Physics, Applied

Аннотация: The problem of ionisation of atomic sodium in the field of resonance laser radiation is numerically solved taking radiative transfer into account. Seed electrons are produced due to the mechanism of associative ionisation, then they gain energy in superelastic processes (collisions of the second kind) and initiate the avalanche ionisation of the medium by electron impact. We studied the effect of secondary radiation on the laser pulse propagation upon competition between the ionising and quenching electron collisions with excited atoms, on the kinetics of ionisation-induced vapour bleaching, and the plasma channel expansion in the form of a halo.


Доп.точки доступа:
Shaparev, N.Ya.; Шапарев, Николай Якимович; Косарев Н.И.

[Text] / A.Zinovyev [et al.] // BMC Syst. Biol. - 2010. - Vol. 4. - Ст. 13, DOI 10.1186/1752-0509-4-13. - Cited References: 66. - We acknowledge support from Agence Nationale de la Recherche (project ANR-08-SYSC-003 CALAMAR) and from the Projet Incitatif Collaboratif "Bioinformatics and Biostatistics of Cancer" at Institut Curie. AZ and EB are members of the team "Systems Biology of Cancer" Equipe labellis'ee par la Ligue Nationale Contre le Cancer. This work was supported by the European Commission Sixth Framework Programme Integrated Project SIROCCO contract number LSHG-CT-2006-037900. We thank Vitaly Volpert and Laurence Calzone for inspiring and useful discussions. . - ISSN 1752-0509РУБ Mathematical & Computational Biology

Аннотация: Background: Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversial messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. Results: In contrary to the study by Nissan and Parker, we show that dynamical data allow discriminating some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data. Conclusions: Our analysis of the transient protein translation dynamics shows that it gives enough information to verify or reject a hypothesis about a particular molecular mechanism of microRNA action on protein translation. For multiscale systems only that action of microRNA is distinguishable which affects the parameters of dominant system (critical parameters), or changes the dominant system itself. Dominant systems generalize and further develop the old and very popular idea of limiting step. Algorithms for identifying dominant systems in multiscale kinetic models are straightforward but not trivial and depend only on the ordering of the model parameters but not on their concrete values. Asymptotic approach to kinetic models allows putting in order diverse experimental observations in complex situations when many alternative hypotheses co-exist.


Доп.точки доступа:
Zinovyev, A.; Morozova, N.; Nonne, N.; Barillot, E.; Harel-Bellan, A.; Gorban, A.N.; Горбань, Александр Николаевич

[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 / A. N. Gorban, O. Radulescu // Advances in Chemical Engineering. - 2008. - Vol. 34 . - p. 103-173DOI 10.1016/S0065-2377(08)00003-3 . -
Аннотация: The concept of the limiting step gives the limit simplification: the whole network behaves as a single step. This is the most popular approach for model simplification in chemical kinetics. However, in its elementary form this idea is applicable only to the simplest linear cycles in steady states. For simple cycles the nonstationary behavior is also limited by a single step, but not the same step that limits the stationary rate. In this chapter, we develop a general theory of static and dynamic limitation for all linear multiscale networks. Our main mathematical tools are auxiliary discrete dynamical systems on finite sets and specially developed algorithms of “cycles surgery” for reaction graphs. New estimates of eigenvectors for diagonally dominant matrices are used. Multiscale ensembles of reaction networks with well-separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors (“modes”) is presented. In particular, we prove that for systems with well-separated constants eigenvalues are real (damped oscillations are improbable). For systems with modular structure, we propose the selection of such modules that it is possible to solve the kinetic equation for every module in the explicit form. All such “solvable” networks are described. The obtained multiscale approximations, that we call “dominant systems” are computationally cheap and robust. These dominant systems can be used for direct computation of steady states and relaxation dynamics, especially when kinetic information is incomplete, for design of experiments and mining of experimental data, and could serve as a robust first approximation in perturbation theory or for preconditioning.

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Доп.точки доступа:
Radulescu, O.; Горбань, Александр Николаевич

[Text] : статья / A. N. Gorban // Physica A. - 2011. - Vol. 390. - p. 1009-1025DOI 10.1016/j.physa.2010.11.030 . -
Аннотация: We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.

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Горбань, Александр Николаевич

[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