Renormalization group in turbulence theory: Exactly solvable Heisenberg model

Theoretical and Mathematical Physics

Volumn 115, Issue 2, 1998, Pages 562-574

  Adzhemyan, L Ts ^a   Antonov, N V ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032356851     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02575456     Document Type: Article

References (38)

1. W. Heisenberg, Z. Phys., 124, 628 (1948).
2. N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantum Fields [in Russian] (4th ed.). Nauka, Moscow (1984), English transl, prev. ed.: Wiley, New York (1959).
3. D. V. Shirkov, Russ. Math. Surv., 49, 155 (1994).
4. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon, Oxford (1989).
5. C. De Dominicis and P. C. Martin, Phys. Rev. A, 19, 419 (1979).
6. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev, Phys. Usp., 39, 1193 (1996).
7. R. H. Kraichnan, Phys. Rev. A, 25, 3281 (1982); Phys. Fluids, 30, 2400 (1987).
8. R. H. Kraichnan, Phys. Rev. A, 25, 3281 (1982); Phys. Fluids, 30, 2400 (1987).
9. S. Chen and R. H. Kraichnan, Phys. Fluids A, 1, 2019 (1989).
10. S. L. Woodruff, Phys. Fluids, 6, 3051 (1994).
11. S. H. Lam, Phys. Fluids A, 4, 1007 (1992).
12. G. L. Eyink, Phys. Fluids, 6, 3063 (1994).
13. E. V. Teodorovich, Fluid Dynamics, No. 4, 517 (1987); Sov. Phys. Dokl., 33, 247 (1988); Izv. Rossiisk. Akad. Nauk, Fiz. Atm. Okeana, 29, 149 (1993).
14. E. V. Teodorovich, Fluid Dynamics, No. 4, 517 (1987); Sov. Phys. Dokl., 33, 247 (1988); Izv. Rossiisk. Akad. Nauk, Fiz. Atm. Okeana, 29, 149 (1993).
15. E. V. Teodorovich, Fluid Dynamics, No. 4, 517 (1987); Sov. Phys. Dokl., 33, 247 (1988); Izv. Rossiisk. Akad. Nauk, Fiz. Atm. Okeana, 29, 149 (1993).
16. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev, JETP, 68, 733 (1989); N. V. Antonov, J. Sov. Math., 54, 873 (1991).
17. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev, JETP, 68, 733 (1989); N. V. Antonov, J. Sov. Math., 54, 873 (1991).
18. N. V. Antonov, S. V. Borisenok, and V. I. Girina, Theor. Math. Phys., 107, 456 (1996).
19. N. V. Antonov, J. Sov. Math., 62, 2950 (1992); Vestn. SPb. Gos. Univ., Fiz. Khim., No. 3, 3 (1992); L. Ts. Adzhemyan, N. V. Antonov, and T. L. Kim, Theor. Math. Phys., 100, 1086 (1994).
20. N. V. Antonov, J. Sov. Math., 62, 2950 (1992); Vestn. SPb. Gos. Univ., Fiz. Khim., No. 3, 3 (1992); L. Ts. Adzhemyan, N. V. Antonov, and T. L. Kim, Theor. Math. Phys., 100, 1086 (1994).
21. N. V. Antonov, J. Sov. Math., 62, 2950 (1992); Vestn. SPb. Gos. Univ., Fiz. Khim., No. 3, 3 (1992); L. Ts. Adzhemyan, N. V. Antonov, and T. L. Kim, Theor. Math. Phys., 100, 1086 (1994).
22. L. Ts. Adzhemyan, A. N. Vasil'ev, and Yu. M. Pis'mak, Theor. Math. Phys., 57, 1131 (1983);
23. L. Ts. Adzhemyan, A. N. Vasil'ev, and M. Gnatich, Theor. Math. Phys., 74, 115 (1988).
24. N. V. Antonov, S. V. Borisenok, and V. I. Girina, Theor. Math. Phys., 106, 75 (1996).
25. N. V. Antonov and A. N. Vasil'ev, Theor. Math. Phys., 110, 97 (1997).
26. M. Avellaneda and A. J. Majda, Commun. Math. Phys., 131, 381 (1990).
27. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics [in Russian], Vol. 2, Mechanics of Turbulence, Gidrometeoizdat, St. Petersburg (1996), English transl, prev. ed.: MIT Press, Cambridge (1975).
28. D. V. Shirkov, Dokl. Akad. Nauk SSSR, 263, 64 (1982); Theor. Math. Phys., 60, 778 (1984); Int. J. Mod. Phys., A3, 1321 (1988).
29. D. V. Shirkov, Dokl. Akad. Nauk SSSR, 263, 64 (1982); Theor. Math. Phys., 60, 778 (1984); Int. J. Mod. Phys., A3, 1321 (1988).
30. D. V. Shirkov, Dokl. Akad. Nauk SSSR, 263, 64 (1982); Theor. Math. Phys., 60, 778 (1984); Int. J. Mod. Phys., A3, 1321 (1988).
31. V. F. Kovalev, V. V. Pustovalov, and D. V. Shirkov, "Group analysis and renormalization group [in Russian]," Preprint JINR P5-95-447, Joint Institute for Nuclear Research, Dubna (1995).
32. N. Goldenfeld, O. Martin, Y. Oono, and F. Liu, Phys. Rev. Lett., 64, 1361 (1990); N. Goldenfeld, O. Martin, and Y. Oono, J. Sci. Comp., 4, 355 (1990).
33. N. Goldenfeld, O. Martin, Y. Oono, and F. Liu, Phys. Rev. Lett., 64, 1361 (1990); N. Goldenfeld, O. Martin, and Y. Oono, J. Sci. Comp., 4, 355 (1990).
34. W. D. McComb, The Physics of Fluid Turbulence, Clarendon, Oxford (1990).
35. J. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion, Cambridge Univ., New Rochelle-Melbourne (1984).
36. V. Yakhot and S. A. Orszag, Phys. Rev. Lett., 57, 1722 (1986); J. Sci. Comput., 1, 3 (1986).
37. V. Yakhot and S. A. Orszag, Phys. Rev. Lett., 57, 1722 (1986); J. Sci. Comput., 1, 3 (1986).
38. W. P. Dannevik, V. Yakhot, and S. A. Orszag, Phys. Fluids, 30, 2021 (1987).