Труды сотрудников ИВМ СО РАН

[Электронный ресурс]. - Электрон. дан. (499 Кб) : диссертации на соискание ученой степени кандидата-физико математических наук (перевод на английский язык) / А.Н. Горбань. - Электрон. дан. (499 Кб). - [Б. м. : б. и.], 1997. - Б. ц.
Аннотация: The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ? of relaxation. This system of times contains: the time before the first entering of the motion into ?-neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the ?-neighbourhood of the limit set. The singularities of relaxation times as functions of (x0; k) under fixed ? are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.

http://icm.krasn.ru/refextra.php?id=2806


Доп.точки доступа:
Gorban A.N.
Свободных экз. нет

[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]. - Electronic data (249 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=788. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/788gorban_AMLappr98.pdf (Полный текст) : статья / A.N. Gorban. - Electronic data (249 Kb) // Applied Mathematics Letters. - 1998. - Vol. 11, № 3. - p. 45-49
   Перевод заглавия: Аппроксимация непрерывных функций нескольких переменных с помощью произвольной нелинейной непрерывной функции одного переменного, линейных функций и их суперпозиций
Аннотация: Linear spaces of continuous functions of real variables closed under the superposition operation are considered. It has been proved that when such a space contains constants, linear functions, and at least one nonlinear function, it is dense in the space of all continuous functions in the topology of uniform convergence on compact sets. So, the approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions is possible.

http://icm.krasn.ru/refextra.php?id=788,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Горбань, Александр Николаевич

[Текст]. - Электрон. дан. (128 Кб)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2083. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/2083gorban_98SOROS.pdf (Полный текст) : статья / А.Н. Горбань. - Электрон. дан. (128 Кб) // Соросовский образовательный журнал. - 1998. - № 12. - С. 105-112
Аннотация: Обсуждается представление функций многих переменных с помощью функций одного переменного. Дано введение в теорию искусственных нейронных сетей. Показано, что с помощью нейросетей можно сколь угодно точно вычислить любую непрерывную функцию.
The following problems on the representation of function of multiple variables by means of simpler functions are discussed: are there functions of multiple variables which cannot be exactly represented by means of functions of one variable and when is an approximate representation of functions using simpler functions possible? An introduction to the theory of artificial neural networks is given. It is shown that with the aid of neural networks one can arbitrarily calculate precisely any continuous function.

http://icm.krasn.ru/refextra.php?id=2083,
Полный текст

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

Доп.точки доступа:
Gorban A.N.

[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,
Полный текст

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

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

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

[Text] : статья / N.V. Erkaev, V.S. Semenov, H.K. Biernat // Nonlinear Processes in Geophysics. - 2002. - Vol. 9, № 2. - p. 131–138 . - ISSN 1023-5809
Аннотация: Magnetic reconnection is an important process providing a fast conversion of magnetic energy into thermal and kinetic plasma energy. In this concern, a key problem is that of the resistive diffusion region where the reconnec-tion process is initiated. In this paper, the diffusion region is associated with a nonuniform conductivity localized to a small region. The nonsteady resistive incompressible MHD equations are solved numerically for the case of symmetric reconnection of antiparallel magnetic fields. A Petschek type steady-state solution is obtained as a result of time relax-ation of the reconnection layer structure from an arbitrary initial stage. The structure of the diffusion region is studied for various ratios of maximum and minimum values of the plasma resistivity. The effective length of the diffusion re-gion and the reconnection rate are determined as functions of the length scale and the maximum of the resistivity. For suf-ficiently small length scale of the resistivity, the reconnection rate is shown to be consistent with Petschek's formula. By increasing the resistivity length scale and decreasing the re-sistivity maximum, the reconnection layer tends to be wider, and correspondingly, the reconnection rate tends to be more consistent with that of the Parker-Sweet regime.

Полный текст,
http://icm.krasn.ru/refextra.php?id=2434

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

Доп.точки доступа:
Semenov, V.S.; Семенов В. С.; Biernat, H.K.; Еркаев, Николай Васильевич

[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

Полный текст

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

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

[Electronic resource]. - Electronic text data : статья / A. N. Gorban. - Electronic text data // Electronic Journal of Differential Equations. - 1997. - Translation of Candidat (Ph.D) Thesis
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.

Полный текст

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

Доп.точки доступа:
Горбань, Александр Николаевич

/ I.V. Stepanova // Commun. Nonlinear Sci. Numer. Simul. - 2013. - Vol. 18, Is. 6. - P1341-1346, DOI 10.1016/j.cnsns.2012.10.013. - Cited References: 14. - Author thanks Prof. V.K. Andreev for formulation of the problem and attention to the work. This work is supported by the Integrational Grant No 44 and The Ministry of education and science of Russia, project 14.A18.21.2014. . - 6. - ISSN 1007-5704РУБ Mathematics, Applied + Mathematics, Interdisciplinary Applications + Mechanics + Physics, Fluids & Plasmas + Physics, Mathematical

Аннотация: Group classification problem is solved for equations of motion of a binary mixture under the buoyancy force and thermodiffusion effect. These equations are parameterized by five arbitrary functions of two arguments. The admissible Lie symmetry algebras of generators are found depending on arbitrary elements. These results are useful for analytical and numerical modeling of the convection in binary mixtures. (C) 2012 Elsevier B. V. All rights reserved.


Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна

/ V.V. Shaidurov, G.I. Shchepanovskaya, V.M. Yakubovich // Russ. J. Numer. Anal. Math. Model. - 2012. - Vol. 27, Is. 6. - pp. 585-601, DOI 10.1515/rnam-2012-0034. - Cited References: 18. - The work was supported by the Russian Foundation for Basic Research (11-01-00224) and by the TRISTAM International project. . - ISSN 0927-6467РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: An algorithm for numerical solution of Navier-Stokes equations for two-dimensional motion of a viscous heat-conducting gas is proposed in the paper. The discretization of the equations is performed by a combination of the method of trajectories for the substantive derivative and the finite element method with piecewise-bilinear basis functions for other summands. Results of numerical study of the supersonic flow structure are presented for a flat channel in its step expansion zone for a wide range of Mach and Reynolds numbers. Velocity and pressure fields are investigated, the vortex structure of the circulation flow is studied in the domain after the step.


Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Shchepanovskaya, G.I.; Щепановская, Галина Ивановна; Yakubovich, M.V.; Якубович, Максим Викторович

/ A.V. Lapko, V.A. Lapko // Optoelectronics, Instrumentation and Data Processing. - 2012. - Vol. 48, Is. 4. - pp. 416-422, DOI 10.3103/S8756699012040139 . - ISSN 8756-6990
Аннотация: Asymptotic properties of a nonparametric estimate of the separating surface equation defined in the space of independent attributes of classified objects are studied. Based on this analysis, the importance of the influence of a priori information about independence of random variables on the approximation properties of the nonparametric decision function in a two-alternative problem of pattern recognition is established. В© 2012 Allerton Press, Inc.

Scopus


Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

[Text] / I. O. Bogulskii, Y. M. Volchkov // Numerical Analysis and Applications. - 2012. - Vol. 5, Is. 2. - pp. 124-128, DOI 10.1134/S1995423912020048 . - ISSN 1995-4239
Аннотация: Numerical schemes for solving two-dimensional dynamic problems of elasticity theory based upon several local approximations for each of the required functions are discussed. The schemes contain free parameters (dissipation constants). An explicit form of artificial dissipation of the solutions allows us to control its size and to effectively construct both explicit and implicit schemes. The principle of producing such schemes is applied to a plane dynamic problem of elasticity theory as an example. We describe a class of problems for which numerical algorithms using several local approximations for each of the required functions are constructed. Examples of solving practical problems are given. В© 2012 Pleiades Publishing, Ltd.

Scopus,
Полный текст


Доп.точки доступа:
Bogulskii, I.O.; Богульский, Игорь Олегович; Volchkov, Y.M.

[Text] / N. Rubab [et al.] // Phys. Plasmas. - 2010. - Vol. 17, Is. 10. - Ст. 103704, DOI 10.1063/1.3491336. - Cited References: 54. - This work is funded by the Higher Education Commission of Pakistan under the HEC-Overseas scholarship program Grant No. Ref: 1-1/PM OS /Phase-II/Batch-I/Austria/2007/. Part of this work was done while N. V. Erkaev was at the Space Research Institute of the Austrian Academy of Sciences in Graz. This work is also supported due to the RFBR Grant No. 09-05-91000-ANF-a. Further support is due to the "Austrian Fonds zur Forderung der Wissenschaftlichen Forschung" under Grant No. P20145-N16. . - ISSN 1070-664XРУБ Physics, Fluids & Plasmas

Аннотация: This study presents a theoretical approach to analyze the influence of kappa distributed streaming ions and magnetized electrons on the plasma wave propagation in the presence of dust by employing two-potential theory. In particular, analytical expressions under certain conditions are derived for various modes of propagation comprising of kinetic Alfven wave streaming instability, two stream instability, and dust acoustic and whistler waves. A dispersion relation for kinetic Alfven-like streaming instability has been derived. The effects of dust particles and Lorentzian index on the growth rates and the threshold streaming velocity for the excitation of the instability are examined. The streaming velocity is observed to be destabilizing for slow motion and stabilizing for fast streaming motions. It is also observed that the presence of magnetic field and superthermal particles hinders the growth rate of instability. Possible applications to various space and astrophysical situations are discussed. (C) 2010 American Institute of Physics. [doi:10.1063/1.3491336]


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

[Text] / N.V. Erkaev, V.S. Semenov, H.K. Biernat // Phys. Plasmas. - 2010. - Vol. 17, Is. 6. - Ст. 60703, DOI 10.1063/1.3439687. - Cited References: 15. - This work is supported by RFBR (Grant Nos. N 07-05-00776-a and N 09-05-91000-ANF_a), and by Program No. 16 of RAS. Additional support is due to the Austrian "Fonds zur Forderung der wissenschaftlichen Forschung" under Project No. I 193-N16 and the "Verwaltungsstelle fur Auslandsbeziehungen" of the Austrian Academy of Sciences. . - ISSN 1070-664XРУБ Physics, Fluids & Plasmas

Аннотация: Hall magnetohydrodynamic model is investigated for current sheet flapping oscillations, which implies a gradient of the normal magnetic field component. For the initial undisturbed current sheet structure, the normal magnetic field component is assumed to have a weak linear variation. The profile of the electric current velocity is described by hyperbolic functions with a maximum at the center of the current sheet. In the framework of this model, eigenfrequencies are calculated as functions of the wave number for the "kink" and "sausage" flapping wave modes. Because of the Hall effects, the flapping eigenfrequency is larger for the waves propagating along the electric current, and it is smaller for the opposite wave propagation with respect to the current. The asymmetry of the flapping wave propagation, caused by Hall effects, is pronounced stronger for thinner current sheets. This is due to the Doppler effect related to the electric current velocity. (C) 2010 American Institute of Physics. [doi:10.1063/1.3439687]


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

[Text] / O.V. Kaptsov // Program. Comput. Softw. - 2010. - Vol. 36, Is. 2. - pp. 97-102, DOI 10.1134/S0361768810020076. - Cited References: 16. - This work was supported by the Russian Foundation for Basic Research, project no. 07-01-00489, and by Siberian Division of Russian Academy of Sciences, integration project no. 103. . - ISSN 0361-7688РУБ Computer Science, Software Engineering

Аннотация: A ring of linear differential operators with smooth coefficients generated by two differentiations is considered. Concepts of operators closed with respect to commutation, a resultant of two operators, and a two-dimensional analogue of Wronskian are introduced. Sufficient conditions that two differential operators are generators of a left ideal annihilating a finite-dimensional space of functions are found. Differential operators annihilating given functions are constructed. The operators obtained transform solutions of one secondorder differential equation into solutions of another equation of the same order.


Доп.точки доступа:
Капцов, Олег Викторович

/ V. V. Shaydurov, G. I. Shchepanovskaya, M. V. Yakubovich // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2013. - Vol. 8236 LNCS: 5th International Conference on Numerical Analysis and Applications, NAA 2012 (15 June 2013 through 20 June 2013, Lozenetz. - P122-131, DOI 10.1007/978-3-642-41515-9_11 . -
Аннотация: The algorithm for numerical solving the Navier-Stokes equations for two-dimensional motion for viscous heat-conducting gas is proposed. The discretization of equations is performed by a combination of a special version of the trajectory method for a substantial derivative and the finite element method with piecewise bilinear basis functions for other terms. The results of numerical studies of the structure of a supersonic flow in a plane channel with an obstacle for a wide range of Mach numbers and Reynolds numbers are presented. Velocity and pressure fields are investigated, and the vortex structure of flow is studied in the circulation area of the obstacle. В© 2013 Springer-Verlag.

Scopus

Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Science, Krasnoyarsk, Russian Federation
Beihang University, Beijing, China

Доп.точки доступа:
Shaydurov, V.V.; Shchepanovskaya, G.I.; Yakubovich, M.V.

[Text] : статья / Yu. V. Shornikov, E. A. Novikov, D. N. Dostovalov, M. S. Myssak // VII IFAC Symposium on Manufacturing Modelling, Management and Control. - Saint Petersburg, 2013. - p. 2185−2190. - (Manufacturing Modelling, Management, and Control ; vol. 7, pt. 1), DOI 10.3182/20130619-3-RU-3018.00252 . - ISBN 978-3-902823-35-9
Аннотация: Peculiarities of computer analysis of discrete-continuous systems in the simulation environment are reviewed. Union of standard elements in the macro blocks and import of nonlinear functions from external applications are used to build block diagrams. Solver is configured for numerical analysis of stiff systems by original methods and supplemented with tools of active computational experiment.

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

Доп.точки доступа:
Novikov, E.A.; Новиков, Евгений Александрович; Dostovalov, D.N.; Myssak, M.S.; Шорников Ю.В.

[Text] : статья / A. V. Lapko, V. A. Lapko // Pattern Recognition and Image Analysis. - 2008. - Vol. 18. - pp. 7-13DOI 10.1134/S1054661808010021 . -
Аннотация: Hybrid systems of pattern recognition are proposed which ensure efficient use of a priori data about the form of decision functions and information of learning samples. The results obtained are generalized for processing heterogeneous data.

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Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

[Text] / T. Penza [et al.] // Planet Space Sci. - 2008. - Vol. 56, Is. 9. - P1260-1272, DOI 10.1016/j.pss.2008.04.005. - Cited References: 53 . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: We investigate the efficiency of the atmospheric mass loss due to hydrodynamic blow-off over the lifetime of the exoplanet HD209458b by studying numerically its hydrogen wind for host star X-ray and EUV (XUV) fluxes between 1 and 100 times that of the present Sun. We apply a time-dependent numerical algorithm which is able to solve the system of hydrodynamic equations straight through the transonic point of the flow including Roche lobe effects. The mass loss rates are calculated as functions of the absorbed energy in the thermosphere. Depending on the heating efficiency for a hydrogen-rich thermosphere the maximum temperature obtained in our study at 1.5R(p1) by neglecting IR cooling is about 5000-10,000 K for heating efficiencies of 10% and 60%, respectively. We find that the upper atmosphere of HD209458b experiences hydrodynamic blow-off even at such low temperatures if one does not neglect gravitational effects caused by the proximity of the planet to its Roche lobe boundary. Depending on the heating efficiency, we find from the solution of the hydrodynamic equations of mass, momentum, and energy balance that energy-limited mass loss rate estimations overestimate the realistic mass loss rate at present time for HD209458b by several times. Using the maximum heating efficiency for hydrogen-rich atmospheres of 60% we find that HD209458b may experience an atmospheric mass loss rate at present time of about 3.5 x 10(10) g s(-1). The mass loss rate evolves to higher values for higher XUV fluxes expected during the early period of the planet's host star evolution, reaching values of several times 10(12) gs(-1). The integrated mass loss is found to be between 1.8% and 4.4% of the present mass of HD209458b. We found that the influence of the stellar tidal forces on atmospheric loss (the Roche lobe effect) is not significant at 0.045 AU. For a similar exoplanet, but at closer orbital distances <= 0.02 AU, the combined effect of the Roche lobe and the high XUV radiation result in much higher thermal loss rates of about 2.6 x 10(11) g s(-1) and even more for early stages. This leads to a total loss over 4 Gyr of 27.5% of the planetary mass. (c) 2008 Elsevier Ltd. All rights reserved.

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Доп.точки доступа:
Penza, T.; Erkaev, N.V.; Еркаев, Николай Васильевич; Kulikov, Y.N.; Langmayr, D.; Lammer, H.; Micela, G.; Cecchi-Pestellini, C.; Biernat, H.K.; Selsis, F.; Barge, P.; Deleuil, M.; Leger, A.