Труды сотрудников ИВМ СО РАН

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

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

[Text]. - Electronic data (45 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2110. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/2110gorban_PREMomMIM98.pdf (Полный текст) : статья / I.V. Karlin, A.N. Gorban, G. Dukek, T.F. Nonnenmacher. - Electronic data (45 Kb) // Physical review E. - 1998. - Vol. 57, № 2. - p. 1668-1672
   Перевод заглавия: Динамические поправки к моментным приближениям
Аннотация: Considering the Grad moment ansatz as a suitable first approximation to a closed finite-moment dynamics, the correction is derived from the Boltzmann equation. The correction consists of two parts, local and nonlocal. Locally corrected thirteen-moment equations are demonstrated to contain exact transport coefficients. Equations resulting from the nonlocal correction give a microscopic justification to some phenomenological theories of extended hydrodynamics

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Полный текст

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

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Dukek, G.; Nonnenmacher, T.F.; Карлин, Илья Вениаминович

[Text] : a Soluble Example / A.N. Gorban, I.V. Karlin // Physical Review Letters. - 1996. - Vol. 77, № 2. - p. 282-285
   Перевод заглавия: Коротковолновой предел гидродинамики: точно решаемый пример
Аннотация: The Chapman-Enskog series for shear stress is summed up in a closed form for a simple model of Grad moment equations. The resulting linear hydrodynamics is demonstrated to be stable for all wavelengths, and the exact asymptotic of the acoustic spectrum in the short-wave domain is obtained.

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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

[Text] : статья / I.V. Karlin, A.N. Gorban // Annelen der Physik. - 2002. - Vol. 11, Iss. 10-11. - p. 783-833DOI 10.1002/1521-3889(200211)11:10/11783::AID-ANDP7833.0.CO;2-V
   Перевод заглавия: Гидродинамика из уравнений Грэда: чему мы можем научиться из точных решений?

ГРНТИ

29.17

Аннотация: A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal kinetic models where the Chapman-Enskog method can be studied exactly, thereby providing the basis to compare various approximations in extending the hydrodynamic description beyond the Navier-Stokes approximation. Various techniques, such as the method of partial summation, Pad_e approximants, and invariance principle are compared both in linear and nonlinear situations.

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Полный текст

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

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

/ H. Lammer [et al.] // Mon. Not. Roy. Astron. Soc. - 2013. - Vol. 430, Is. 2. - P1247-1256, DOI 10.1093/mnras/sts705. - Cited References: 85. - NVE, KGK, MLK and HL acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets' and S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. KGK, HL and PO thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. ML and PO acknowledge support from the FWF project P22950-N16. NVE acknowledges support by the RFBR grant No 12-05-00152-a. The authors also acknowledge support from the EU FP7 project IMPEx (No. 262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science working group WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, we thank an anonymous referee for interesting suggestions and recommendations which helped to improve the article. . - 10. - ISSN 0035-8711РУБ Astronomy & Astrophysics

Аннотация: The discovery of transiting 'super-Earths' with inflated radii and known masses, such as Kepler-11b-f, GJ 1214b and 55 Cnc e, indicates that these exoplanets did not lose their nebula-captured hydrogen-rich, degassed or impact-delivered protoatmospheres by atmospheric escape processes. Because hydrodynamic blow-off of atmospheric hydrogen atoms is the most efficient atmospheric escape process we apply a time-dependent numerical algorithm which is able to solve the system of 1D fluid equations for mass, momentum and energy conservation to investigate the criteria under which 'super-Earths' with hydrogen-dominated upper atmospheres can experience hydrodynamic expansion by heating of the stellar soft X-rays and extreme ultraviolet (XUV) radiation and thermal escape via blow-off. Depending on orbit location, XUV flux, heating efficiency and the planet's mean density our results indicate that the upper atmospheres of all 'super-Earths' can expand to large distances, so that except for Kepler-11c all of them experience atmospheric mass-loss due to Roche lobe overflow. The atmospheric mass loss of the studied 'super-Earths' is one to two orders of magnitude lower compared to that of 'hot Jupiters' such as HD 209458b, so that one can expect that these exoplanets cannot lose their hydrogen envelopes during their remaining lifetimes.


Доп.точки доступа:
Lammer, H.; Erkaev, N.V.; Еркаев, Николай Васильевич; Odert, P.; Kislyakova, K.G.; Leitzinger, M.; Khodachenko, M.L.

[Text] / N. V. Erkaev [et al.] // Astron. Astrophys. - 2007. - Vol. 472, Is. 1. - P329-334, DOI 10.1051/0004-6361:20066929. - Cited References: 26 . - ISSN 0004-6361РУБ Astronomy & Astrophysics

Аннотация: Context. A study of the mass loss enhancement for very close "Hot Jupiters" due to the gravitational field of the host star is presented. Aims. The influence of the proximity to a planet of the Roche lobe boundary on the critical temperature for blow-off conditions for estimating the increase of the mass loss rate through hydrodynamic blow-off for close-in exoplanets is investigated. Methods. We consider the gravitational potential for a star and a planet along the line that joins their mass centers and the energy balance equation for an evaporating planetary atmosphere including the effect of the stellar tidal force on atmospheric escape. Results. By studying the effect of the Roche lobe on the atmospheric loss from short-periodic gas giants we derived reasonably accurate approximate formulas to estimate atmospheric loss enhancement due to the action of tidal forces on a "Hot Jupiter" and to calculate the critical temperature for the onset of "geometrical blow-off", which are valid for any physical values of the Roche lobe radial distance. Using these formulas, we found that the stellar tidal forces can enhance the hydrodynamic evaporation rate from TreS-1 and OGLE-TR-56b by about 2 fold, while for HD 209458b we found an enhancement of about 50%. For similar exoplanets which are closer to their host star than OGLE-TR-56b, the mass loss enhancement can be even larger. Moreover, we showed that the effect of the Roche lobe allows "Hot Jupiters" to reach blow-off conditions at temperatures which are less than expected due to the stellar X-ray and EUV heating.


Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Kulikov, Y.N.; Lammer, H.; Selsis, F.; Langmayr, D.; Jaritz, G.F.; Biernat, H.K.

[Text] : статья / I. V. Karlin, M. Colangeli, M. Kröger // Physical review letters. - 2008. - Vol. 100. - Ст. 214503DOI 10.1103/PhysRevLett.100.214503 . -
Аннотация: Exact (to all orders in Knudsen number) equations of linear hydrodynamics are derived from the Boltzmann kinetic equation with the Bhatnagar-Gross-Krook collision integral. The exact hydrodynamic equations are cast in a form which allows us to immediately prove their hyperbolicity, stability, and existence of an H theorem.

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Доп.точки доступа:
Colangeli, M.; Kröger, M.; Карлин, Илья Вениаминович

[Text] : статья / W. P. Yudistiawan, S. Ansumali, I. V. Karlin // Physical review E. - 2008. - Vol. 78. - Ст. 016705, DOI 10.1103/PhysRevE.78.016705 . - ISSN 1539-3755
Аннотация: Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali et al., Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation—the nine-bit model in two dimensions—in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

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

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

[Text] : статья / V. B. Bekezhanova // Fluid Dynamics. - 2011. - Vol. 46, Iss. 4. - p. 525-535DOI 10.1134/S001546281104003X . -
Аннотация: A plane steady-state two-layer fluid flow under the coupled action of the buoyancy and Marangoni forces is considered. The system is oriented at an arbitrary angle with respect to the gravity force. Exact solutions generalizing the Ostroumov-Birikh solution are obtained and their stability is studied in the framework of a linear theory. On the basis of numerical calculations, the influence of the inclination angle, the thickness of the layers, and the wall heating conditions on the instability mechanisms is investigated.

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Доп.точки доступа:
Бекежанова, Виктория Бахытовна

[Text] / H. . Lammer [et al.] // Mon. Not. Roy. Astron. Soc. - 2014. - Vol. 439, Is. 4. - P. 3225-3238, DOI 10.1093/mnras/stu085. - Cited References: 75. - The authors acknowledge the support by the FWF NFN project S11601-N16 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S 116 02-N16 'Hydrodynamics in Young Star-Disk Systems', S116 604-N16 'Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond', and S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. KGK, YNK, HL, and PO thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. ML and PO acknowledge support from the FWF project P22950-N16. NVE acknowledges support by the RFBR grant no. 12-05-00152-a. Finally, the authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar-and exoplanetary environments'. . - ISSN 0035-8711. - ISSN 1365-2966РУБ Astronomy & Astrophysics

Аннотация: We investigate the origin and loss of captured hydrogen envelopes from protoplanets having masses in a range between 'sub-Earth'-like bodies of 0.1 M-circle plus and 'super-Earths' with 5 M-circle plus in the habitable zone at 1 au of a Sun-like G star, assuming that their rocky cores had formed before the nebula gas dissipated. We model the gravitational attraction and accumulation of nebula gas around a planet's core as a function of protoplanetary luminosity during accretion and calculate the resulting surface temperature by solving the hydrostatic structure equations for the protoplanetary nebula. Depending on nebular properties, such as the dust grain depletion factor, planetesimal accretion rates, and resulting luminosities, for planetary bodies of 0.1-1 M-circle plus we obtain hydrogen envelopes with masses between similar to 2.5 x 10(19) and 1.5 x 10(26) g. For 'super-Earths' with masses between 2 and 5 M-circle plus more massive hydrogen envelopes within the mass range of similar to 7.5 x 10(23)-1.5 x 10(28) g can be captured from the nebula. For studying the escape of these accumulated hydrogen-dominated protoatmospheres, we apply a hydrodynamic upper atmosphere model and calculate the loss rates due to the heating by the high soft-X-ray and extreme ultraviolet (XUV) flux of the young Sun/star. The results of our study indicate that under most nebula conditions 'sub-Earth' and Earth-mass planets can lose their captured hydrogen envelopes by thermal escape during the first similar to 100 Myr after the disc dissipated. However, if a nebula has a low dust depletion factor or low accretion rates resulting in low protoplanetary luminosities, it is possible that even protoplanets with Earth-mass cores may keep their hydrogen envelopes during their whole lifetime. In contrast to lower mass protoplanets, more massive 'super-Earths', which can accumulate a huge amount of nebula gas, lose only tiny fractions of their primordial hydrogen envelopes. Our results agree with the fact that Venus, Earth, and Mars are not surrounded by dense hydrogen envelopes, as well as with the recent discoveries of low density 'super-Earths' that most likely could not get rid of their dense protoatmospheres.

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Держатели документа:
ИВМ СО РАН

Доп.точки доступа:
Lammer, H.; Stokl, A.; Erkaev, N.V.; Еркаев, Николай Васильевич; Dorfi, E.A.; Odert, P.; Gudel, M.; Kulikov, Y.N.; Kislyakova, K.G.; Leitzinger, M.; FWF NFN [S11601-N16, S 116 02-N16, S116 604-N16, S116607-N16]; FWF [P22950-N16]; RFBR [12-05-00152-a]

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

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

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

/ Z. I. Fedotova, E. D. Karepova // Russ. J. Numer. Anal. Math. Model. - 1996. - Vol. 11, Is. 3. - P183-204, DOI 10.1515/rnam.1996.11.3.183. - Cited References: 15 . - ISSN 0927-6467РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: In work we describe one of the methods of constructing approximate hydrodynamic models with the supposition of a long wave nature of now. This method allows us to derive a nonlinear dispersive model to obtain its variational wording. We consider the general case of hydrodynamic equations for a potential ideal fluid flow over an irregular bottom as well as some special cases.

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Держатели документа:
Computer Center, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Fedotova, Z.I.; Karepova, E.D.; Карепова, Евгения Дмитриевна

[Text] / I. V. Karlin, G. . Dukek, T. F. Nonnenmacher // Phys. Rev. E. - 1997. - Vol. 55, Is. 2. - P1573-1576, DOI 10.1103/PhysRevE.55.1573. - Cited References: 6 . - ISSN 1063-651XРУБ Physics, Fluids & Plasmas + Physics, Mathematical

Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].

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

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

/ I. V. Karlin, G. Dukek, T. F. Nonnenmacher // Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. - 1997. - Vol. 55, Is. 2. - P1573-1576 . - ISSN 1063-651X
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].

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

[Text] / S. . Succi, H. . Chen, I. . Karlin // J. Phys. IV. - 1998. - Vol. 8: Conference on Disorder and Chaos in Honour and Memory of Giovanni Paladin (SEP 22-24, 1997, ROME, ITALY), Is. P6. - P271-275, DOI 10.1051/jp4:1998637. - Cited References: 11 . - ISSN 1155-4339РУБ Physics, Multidisciplinary

Аннотация: We discuss some internal symmetries of lattice hydrodynamics and point out possible analogies with statistical field theory.

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Держатели документа:
Ist Applicaz Calcolo, Rome, Italy
EXA Corp, Boston, MA USA
RAS, Ctr Comp, Krasnoyarsk, Russia
ИВМ СО РАН

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

/ I. F. Shaikhislamov [et al.] // Astrophys. J. - 2014. - Vol. 795, Is. 2, DOI 10.1088/0004-637X/795/2/132 . - ISSN 0004-637X
Аннотация: In the present series of papers we propose a consistent description of the mass loss process. To study in a comprehensive way the effects of the intrinsic magnetic field of a close-orbit giant exoplanet (a so-called hot Jupiter) on atmospheric material escape and the formation of a planetary inner magnetosphere, we start with a hydrodynamic model of an upper atmosphere expansion in this paper. While considering a simple hydrogen atmosphere model, we focus on the self-consistent inclusion of the effects of radiative heating and ionization of the atmospheric gas with its consequent expansion in the outer space. Primary attention is paid to an investigation of the role of the specific conditions at the inner and outer boundaries of the simulation domain, under which different regimes of material escape (free and restricted flow) are formed. A comparative study is performed of different processes, such as X-ray and ultraviolet (XUV) heating, material ionization and recombination, H+ 3 cooling, adiabatic and Lyα cooling, and Lyα reabsorption. We confirm the basic consistency of the outcomes of our modeling with the results of other hydrodynamic models of expanding planetary atmospheres. In particular, we determine that, under the typical conditions of an orbital distance of 0.05AU around a Sun-type star, a hot Jupiter plasma envelope may reach maximum temperatures up to ∼9000K with a hydrodynamic escape speed of ∼9 km s-1, resulting in mass loss rates of ∼ (4-7) · 1010 g s-1. In the range of the considered stellar-planetary parameters and XUV fluxes, that is close to the mass loss in the energy-limited case. The inclusion of planetary intrinsic magnetic fields in the model is a subject of the follow-up paper (Paper II).

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Держатели документа:
Institute of Computational Modelling, SB RASKrasnoyarsk, Russian Federation

Доп.точки доступа:
Shaikhislamov, I.F.; Khodachenko, M.L.; Sasunov, Y.L.; Lammer, H.; Kislyakova, K.G.; Erkaev, N.V.; Еркаев, Николай Васильевич

/ T. I. Maindl [et al.] // Astron. Astrophys. - 2015. - Vol. 574, DOI 10.1051/0004-6361/201424256 . - ISSN 0004-6361
Аннотация: Aims. We investigate the influence of impacts of large planetesimals and small planetary embryos on the early Martian surface on the hydrodynamic escape of an early steam atmosphere that is exposed to the high soft X-ray and extreme-ultraviolet (EUV) flux of the young Sun. Methods. Impact statistics in terms of number, masses, velocities, and angles of asteroid impacts onto early Mars are determined via n-body integrations. Based on these statistics, smoothed particle hydrodynamics (SPH) simulations result in estimates of energy transfer into the planetary surface material and the resulting surface heating. For the estimation of the atmospheric escape rates we applied a soft X-ray and EUV absorption model and a 1D upper atmosphere hydrodynamic model to a magma ocean-related catastrophically outgassed steam atmosphere with surface pressure values of 52 bar H2O and 11 bar CO2. Results. The estimated impact rates and energy deposition onto an early Martian surface can account for substantial heating. The energy influx and conversion rate into internal energy is probably sufficient to keep a shallow magma ocean liquid for an extended period of time. Higher surface temperatures keep the outgassed steam atmosphere longer in vapor form and therefore enhance its escape to space within ?0.6 Myr after its formation.

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Держатели документа:
Institute for Computational Modelling, Russian Academy of SciencesKrasnoyarsk 36, Russian Federation

Доп.точки доступа:
Maindl, T.I.; Dvorak, R.; Lammer, H.; Gudel, M.; Schafer, C.; Speith, R.; Odert, P.; Erkaev, N.V.; Еркаев, Николай Васильевич; Kislyakova, K.G.; Pilat-Lohinger, E.

[Text] / N. V. Erkaev [et al.] // Mon. Not. Roy. Astron. Soc. - 2015. - Vol. 448, Is. 2. - P1916-1921, DOI 10.1093/mnras/stv130. - Cited References:28. - The authors acknowledge the support by the FWF NFN project S11601-N16 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subproject, S11607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. PO acknowledges support from the FWF project P22950-N16. NVE acknowledges support by the RFBR grant no. 15-05-00879-a. Finally, the authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar-and exoplanetary environments'. . - ISSN 0035-8711. - ISSN 1365-2966РУБ Astronomy & Astrophysics

Аннотация: By considering martian-like planetary embryos inside the habitable zone of solar-like stars we study the behaviour of the hydrodynamic atmospheric escape of hydrogen for small values of the Jeans escape parameter beta < 3, near the base of the thermosphere, that is defined as a ratio of the gravitational and thermal energy. Our study is based on a 1D hydrodynamic upper atmosphere model that calculates the volume heating rate in a hydrogen-dominated thermosphere due to the absorption of the stellar soft X-ray and extreme ultraviolet (XUV) flux. In case of a monatomic gas, we find that when the beta value near the mesopause/homopause level exceeds a critical value of similar to 2.5, there exists a steady hydrodynamic solution with a smooth transition from subsonic to supersonic flow. For a fixed XUV flux, the escape rate of the upper atmosphere is an increasing function of the temperature at the lower boundary. Our model results indicate a crucial enhancement of the atmospheric escape rate, when the Jeans escape parameter beta decreases to this critical value. When beta becomes <= 2.5, there is no stationary hydrodynamic transition from subsonic to supersonic flow. This is the case of a fast non-stationary atmospheric expansion that results in extreme thermal atmospheric escape rates.

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Держатели документа:
Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Krasnoyarsk 660041, Russia.
Austrian Acad Sci, Space Res Inst, A-8042 Graz, Austria.
Graz Univ, Inst Phys, A-8010 Graz, Austria.
Russian Acad Sci, Polar Geophys Inst, Murmansk 183010, Russia.
ИВМ СО РАН

Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Lammer, H.; Odert, P.; Kulikov, Yu. N.; Kislyakova, K.G.; FWF NFN [S11601-N16, S11607-N16]; FWF [P22950-N16]; RFBR [15-05-00879-a]

[Text] : статья / V. A. Ivanov, N. V. Erkaev, D. Langmayr // Журнал Сибирского федерального университета. Серия: Техника и технологии. - 2015. - Т. 8, № 3. - С. 270-282 . - ISSN 1999-494X
   Перевод заглавия: Гидродинамический подшипник скольжения: моделирование упругих деформаций
Аннотация: This article deals with a new approach for calculation of self-consistent pressure distribution and surface de?ection for a lubricated journal bearing. This approach is based on the numerical solution of the 2-D Reynolds’ equation for the lubrication layer, numerical calculation of the surface deformations by the 3-D ANSYS package and Fourier series expansion for the compliance matrix. A simple analytical approximation is found for the obtained compliance matrix, which can be used for heavy loaded journal bearings. The compliance matrix is implemented into the iterative procedure for calculation of self-consistent pressure distribution and surface de?ection in the contact zone. Results of calculations are presented for the particular journal bearing.
В статье рассмотрен новый подход к вычислению самосогласованного распределения давления и деформации поверхности для цилиндрического подшипника скольжения. Предлагаемый метод основан на численном решении 2-мерного уравнения Рейнольдса для смазочного слоя, вычислении деформации поверхности с помощью 3-мерного пакета АНСИС с использованием разложения Фурье для вычисления матрицы податливости. Найдена простая аналитическая аппроксимация для матрицы податливости, которая может применяться для расчета тяжело нагруженных подшипников скольжения. Найденная матрица податливости используется в итеративной процедуре для расчета самосогласованного распределения давления и прогиба поверхности в зоне контакта. Представлены результаты расчета конкретного подшипника скольжения.

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Держатели документа:
ANSYS Germany GmbH
Institute of Computational Modelling SB RAS
Siberian Federal University

Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Langmayr, D.; Лангмайр Д.; Иванов В.А.

/ B. D. Annin, V. A. Kovtunenko, V. M. Sadovskii // Springer Proceedings in Mathematics and Statistics. - 2015. - Vol. 121: 2nd International Conference on Applied Mathematics and Informatics, ICAMI 2013 (24 November 2013 through 29 November 2013, ) Conference code: 136889. - P49-56, DOI 10.1007/978-3-319-12583-1_3 . -
Аннотация: This contribution is devoted to the mathematical theory of elastoplastic and granular solids as well as the quasibrittle fracture of nonlinear cracks. Basic variational and hemivariational inequalities describing nonlinear phenomena due to plasticity, internal friction, interfacial interaction, and alike dissipative physics are outlined from the point of view of nonsmooth and nonconvex optimization. Primary results of the nonlinear theory and its application to solid mechanics are surveyed. © Springer International Publishing Switzerland 2015.

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Держатели документа:
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstr. 36, Graz, Austria
Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russian Federation
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Annin, B. D.; Kovtunenko, V. A.; Sadovskii, V. M.