On the n-theorem for systems of chemical kinetics with continuous and discrete time and on the system of equations of nucleosynthesis

 
PIIS004446690002530-4-1
DOI10.31857/S004446690002530-4
Publication type Article
Status Published
Authors
Affiliation: Moscow State University M. V. Lomonosova
Address: Russian Federation
Affiliation: IMP RAS
Address: Russian Federation
Affiliation: RUDN
Address: Russian Federation
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 9
Pages1517-1530
Abstract

  

Keywords
AcknowledgmentThis work was financially supported by the Ministry of Education and Science of the Russian Federation under the program of enhancing the competitiveness of PFUR “5-100” among the world's leading scientific and educational centers for 2016–2020. and with the support of the program of the OMS of the RAS 1.3.1 problems of computational mathematical physics.
Received19.12.2018
Publication date19.12.2018
Cite   Download pdf To download PDF you should sign in
Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

views: 1096

Readers community rating: votes 0

1. Bol'tsman L. Dal'nejshie issledovaniya teplovogo ravnovesiya mezhdu molekulami gaza // Izbrannye trudy. M.: Nauka, 1984. S. 125–189.

2. Bol'tsman L. O svyazi mezhdu vtorym nachalom mekhanicheskoj teorii teploty i teoriej veroyatnostej v teoremakh o teplovom ravnovesii. Izbrannye trudy. M.: Nauka, 1984. S. 190–235.

3. Godunov S.K., Sultangazin U.M. O diskretnykh modelyakh kineticheskogo uravneniya Bol'tsmana // Uspekhi matem. nauk. 1971. T. 26. № 3 (159). C. 3–51.

4. Vedenyapin V.V. Kineticheskie uravneniya Bol'tsmana i Vlasova. M.: Fizmatlit, 2001. 112 s.

5. Vol'pert A.I., Khudyaev S.I. Analiz v klassakh razryvnykh funktsij i uravneniya matematicheskoj fiziki. M.: Nauka, 1975. 394 s.

6. Batischeva Ya.G., Vedenyapin V.V. II-j zakon termodinamiki dlya khimicheskoj kinetiki // Matem. modelirovanie. 2005. T. 17. № 8. S. 106–110.

7. Vedenyapin V.V., Orlov Yu.N. O zakonakh sokhraneniya dlya polinomial'nykh gamil'tonianov i dlya diskretnykh modelej uravneniya Bol'tsmana // Teor. i matem. fiz. 1999. T. 121. № 2. S. 307–315.

8. Vedenyapin V.V., Adzhiev S.Z. Ehntropiya po Bol'tsmanu i Puankare // Uspekhi matem. nauk. 2014. T. 69. № 6. S. 45–80.

9. Mozer Yu. Lektsii o gamil'tonovykh sistemakh. M.: Mir, 1973. 168 s.

10. Bryuno A.D. Ogranichennaya zadacha trekh tel. Ploskie periodicheskie orbity. M.: Nauka, 1990. 296 s.

11. Adzhiev S., Melikhov I., Vedenyapin V. The H-theorem for the chemical kinetic equations with discrete time and for their generalizations // J. Physics: Conference Series. 2017. V. 788. № 1. S. 012001.

12. Adzhiev S.Z., Melikhov I.V., Vedenyapin V.V. The H-theorem for the physico-chemical kinetic equations with discrete time and for their generalizations // Physica A: Statistical Mechanics and its Applicat. 2017. V. 480. P. 39–50.

13. Adzhiev S.Z., Melikhov I.V., Vedenyapin V.V. The H-theorem for the physico-chemical kinetic equations with explicit time discretization // Physica A: Statistical Mechanics and its Applicat. 2017. V. 481. P. 60–69.

14. Eremin A.Yu., Mar'yashkin N.Ya., Sinyukova O.N., Tygliyan A.V., Filippov S.S., Chechetkin V.M. Chislennoe modelirovanie kinetiki obrazovaniya tyazhelykh ehlementov: postanovka zadachi i metod rascheta: Preprint № 21. M.: IPM AN SSSR. 1981.

15. Burbidge E.M., Burbidge G.R., Fowler W.A., Hoyle F. Synthesis of the elements in Stars // Revs. Mod. Phys. 1957. V. 29. № 4. P. 547–650.

16. Fauler U., Khojl F. Nejtrinnye protsessy i obrazovanie par v massivnykh zvezdakh i sverkhnovykh. M.: Mir, 1976.

17. Blake J.B., Schramm D.N. A consideration of the neutron capture time scale in the s-process // Astrophys. J. 1975. V. 197. № 3. 615.

18. Ward R.A., Newman M.J., Clayton D.D. S-process Studies: Branching and the Time Scale // Astrophys. J. 1976. V. 205. № 2. 655.

19. Seeger P.A., Fowler W.A., Clayton D.D. Nucleosynthesis of heavy elements by neutron capture // The Astrophysical Journal Supplement. 1965. V. 11. P. 121–166.

20. Schramm D.N., Norman E.B. Heavy Element Nucleosynthesis // Proceedings of the 3-rd International Conference on Nuclei far from Stability. Cern 76-13, Geneva, 1976. P. 570.

21. Ivanova L.H., Imshennik V.S., Chechetkin B.M. Chislennye raschety termoyadernogo vzryva vyrozhdennogo uglerodnogo yadra zvezdy // Astronom. zh. 1977. T. 54. № 3. C. 661.

22. Janecke J., Eynon B.P. Masses from inhomogeneous partial difference equations // Atomic Data and Nucl. Data Tables. 1976. V. 17. P. 46 7–473.

23. Myers W. D., Swiatecki W.J. Average nuclear properties // Ann. Phys. 1969. V. 55. 395.

24. Gear C.W. The automatic integrating of stiff ordinary differential equations. Information Proc. 68, “North-Holland Publishing Company”, Amsterdam, 1969. P. 187.

25. Gol'berg S.M., Zakharov A.Yu., Filippov S.S. O nekotorykh chislennykh metodakh resheniya zhestkikh sistem obyknovennykh differentsial'nykh uravnenij: Preprint № 12. M.,IPM AN SSSR. 1976.

26. Gibbs N.E., Poole W.G.-jr., Stockmeyer P.K. An Algorithm for Reducing the Bandwidth And Profile of a Sparse Matrix // SIAM J. Numer. Anal. 1976. V. 13. № 2. P. 236.

27. Bobylev A.V., Cercignani C. Discrete velocity models for mixtures // J. Statist. Phys. 1998. V. 91. № 1/2. P. 327–341.

28. Vedenyapin V.V. Velocity inductive construction for mixtures // Transp. Theory and Statist. Phys. 1999. V. 28. № 7. P. 727–742.

29. Vedenyapin V.V., Amosov S.A., Toskano L. Invarianty dlya gamil'tonianov i kineticheskikh uravnenij // Uspekhi matem. nauk. 1999. T. 54. № 5. S. 153–154.

30. Vedenyapin V.V., Amosov S.A., Toskano L. Diskretnye modeli uravneniya Bol'tsmana dlya smesej // Matem. modelirovanie. 2000. № 7. S. 18–22.

31. Amossov S.A. Two-level discrete models of Boltzmann equation for binary mixtures // Transp. Theory and Statist. Phys. 2002. V. 31. № 2. P. 125–139.

32. Vedenyapin V.V., Amosov S.A. O diskretnykh modelyakh uravneniya Bol'tsmana dlya smesej // Differents. ur-niya. 2000. T. 36. № 7. S. 15–20.

33. Amossov S.A. Discrete models of relativistic Boltzmann equation for mixtures // Physica A: Statistical Mechanics and Its Applications. 2001. V. 301. № 1. P. 330–340.

34. Adzhiev S.Z., Amosov S.A., Vedenyapin V.V. Odnomernye diskretnye modeli kineticheskikh uravnenij dlya smesej // Zh. vychisl. matem. i matem. fiz. 2004. T. 44. № 3. S. 553–558.

35. Adzhiev S.Z., Vedenyapin V.V. O razmerakh diskretnykh modelej uravneniya Bol'tsmana dlya smesej // Zh. vychisl. matem. i matem. fiz. 2007. T. 47. № 6. S. 1045–1054.

36. Bobylev A.V., Vinerean M.C. Construction of discrete kinetic models with given invariants // J. Stat. Phys. 2008. V. 132. № 1. P. 153–170.

37. Gasnikov A.V., Gasnikova E.V. Ob ehntropijno-podobnykh funktsionalakh, voznikayuschikh v stokhasticheskoj khimicheskoj kinetike pri kontsentratsii invariantnoj mery i v kachestve funktsij Lyapunova dinamiki kvazisrednikh // Matem. zametki. 2013. T. 94. № 6. C. 819–827.

Система Orphus

Loading...
Up