Renormalization group and instantons in stochastic nonlinear dynamics

European Physical Journal: Special Topics

Volumn 170, Issue 1, 2009, Pages 1-142

  Volchenkov, D ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

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EID: 65249102207     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2009-01001-3     Document Type: Review

References (189)

1. P. Sagaut, C. Cambon, Homogeneous Turbulence Dynamics (Cambridge University Press, Cambridge, 2009)
2. L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasiliev, Phys. Usp. 39, 1193 (1996) (in Russian)
3. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, Vol. 2 (MIT Press, Cambridge, MA, 1971, 1975)
4. R.H. Kraichnan, J. Fluid Mech. 5, 407 (1959)
5. H.W. Wyld, Ann. Phys. 14, 143 (1961)
6. L.Ts. Adzhemyan, N.V. Antonov, P.B. Gol'din, T.L. Kim, M.V. Kompaniets, J. Phys. A 41, 495002 (2008)
7. A.N. Kolmogorov, Dokladi Akad. Nauk USSR 30, 299 (1941)
8. A.M. Obukhov, Dokladi Akad. Nauk USSR 32, 22 (1941)
9. A.N. Vasil'ev, Functional Methods in Quantum Field theory and Statistics (Gordom and Breach, NY, 1998)
10. R.H. Kraichnan, J. Fluid Mech. 7, 1723 (1965)
11. R.H. Kraichnan, J. Fluid Mech. 8, 575 (1966)
12. R.H. Kraichnan, J. Fluid Mech. 9, 1728, 1884 (1968)
13. H.K. Janssen, Z. Phys. B 23, 377 (1976)
14. C. de Dominicis, J. Phys. (France) 37, 247 (1976)
15. C. de Dominicis, L. Peliti, Phys. Rev. B 18, 353 (1978)
16. R. Phythian, J. Phys. A 10, 777 (1977)
17. J. Collins, Renormalization: An Introduction to Renormalization, the Renormalization Group, and the Operator - Product Expansion (Cambridge University Press, Cambridge, 1992)
18. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1990)
19. N.N. Bogolubov, D.V. Shirkov, Introduction to the Theory of Quantum Fields, 3rd edn. (Wiley, New York, 1980)
20. C. De Dominicis, P.C. Martin, Phys. Rev. A 19, 419 (1979)
21. E. Jurcisinova, M. Jurcisin, R. Remecky, M. Scholtz, The Seventh Small Triangle Meeting, Herlany, September 17-20 (2006)
22. N.V. Antonov, A.A. Ignatieva, J. Phys. A 39, 13593 (2006)
23. L.Ts. Adzhemyan, A.N. Vasil'ev, Yu.M. Pis'mak, Theor. Math. Phys. 57, 1131 (1983)
24. L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasiliev, Sov. Phys. JETP 68, 733 (1989)
25. L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasiliev, Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach, New York, 1998)
26. D. Volchenkov, M. Nalimov, Theor. Math. Phys. 106, 307 (1996)
27. L.Ts. Adzhemnyan, M.Yu. Nalimov, M.M. Stepanova, Theor. Math. Phys. 104, 260 (1995)
28. V.S. L'vov, A.V. Michailov, Preprint N54 (Institute of Automatics and Electrotechnics, Novosibirsk, 1977) (in Russian)
29. I. Staroselsky, V. Yakhot, S. Kida, A.S. Orszag, Phys. Rev. Lett. 65, 171 (1990)
30. P.C. Martin, E.D. Siggia, H.A. Rose, Phys. Rev. A 8, 423 (1973)
31. R. Bausch, H.K. Janssen, H. Wagner, Z. Phys. B 24, 113 (1976)
32. G.I. Taylor, Proc. Roy. Soc. A 20, 196 (1921)
33. P. Legentilhomme, J. Legrand, J. Comiti, J. Appl. Electrochem. 19, 263 (1989)
34. A.M. Obukhov, Sov. Phys. Uspekhi 138 (1962)
35. G. Erochenkova, R. Lima, Physica A 275, 297 (2000)
36. G. Erochenkova, R. Lima, Chaos 11, 495 (2001)
37. R.A. Greenkorn, Flow Phenomena in Porous Media (Marcel Dekker Inc., 1983)
38. J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972)
39. S. Whitaker, Transp. Porous Media 1, 3 (1986)
40. N.V. Antonov, M. Hnatich, J. Honkonen, J. Phys. A 39, 7867 (2006)
41. L.Ts. Adzhemyan, A.N. Vasil'ev, Yu.M. Pis'mak, Theor. Math. Phys. 68, 770 (1987)
42. A. Munster, Statistical Thermodynamics (Springer, Berlin, 1969)
43. A.M. Obukhov, Izvestia Akad. Nauk USSR: Geogr. Geophys. 13, 58 (1949)
44. R.H. Kraichnan, Phys. Fluids 11, 945 (1968)
45. N.V. Antonov, Sov. Phys. JTEP 105, 614 (1994)
46. L.Ts. Adjemyan, A.N. Vasil'ev, N.V. Antonov, Phys. Rev. E 58, 1823 (1998)
47. M. Hnatich, Theor. Math. Phys. 83, 374 (1990)
48. N.V. Antonov, Sov. Phys. JTEP 112, 1649 (1997)
49. D. Volchenkov, R. Lima, Chaos 10, 711 (2000)
50. R. Lima, D. Volchenkov, The Science of Complexity: From Mathematics to Technology to a Sustainable World, Paper 023, avail. at http://www.physik.uni-bielefeld.de/complexity/, ©Zentrum für Interdisciplinäre Forschung, Bielefeld, Allemagne (2002)
51. V.P. Krasitskii, J. Fluid Mech. 272, 1 (1994)
52. W. Diehl, S. Dietrich, Z. Phys. B 2, 65 (1981)
53. E. Brézin, S. Leibler, Phys. Rev. B 27, 595 (1983)
54. S.K. Ma, Modern Theory of Critical Phenomena (Benjamin Reading, 1976)
55. A.S. Monin, V.P. Krasitskii, Phenomena on the Ocean Surface (Saint-Petersburg, Gidrometeoizdat, 1985)
56. E. Brézin, J.C. Le Guillou, J. Zinn-Justin, in Phase Transitions and Critical Phenomena Vol. 6, edited by C. Domb, M.S. Green (Academic Press, London, 1976)
57. M. Guidry, Gauge Field Theories (John Wiley Publ., New York, 1991)
58. E. Leader, E. Predazzi, An Introduction to Gauge Theory and Modern Particle Physics (Cambridge University Press, Cambridge, 1996)
59. V.M. Kamenkovich, M.N. Koshlyakov, A.S. Monin, Synoptic Eddies in Oceans (Gidrometeoizdat, St.-Peterburg, 1982)
60. E. Brézin, D.J. Wallace, K.G. Wilson, Phys. Rev. B 7, 232 (1973)
61. B.S. de Witt, Phys. Rev. 162, 1195 (1967)
62. A.M. Polyakov, Gauge Fields and Strings, in Contemporary Concepts in Physics, Vol. 3 (Harwood Acad. Publ., 1987)
63. G.'t Hooft, Advanced Series in Mathematical Physics, Vol. 19 (World Scientific, 1994)
64. S. Coleman, in Laws of Hadronic Matter, edited by A. Zichichi (Academic Press, 1975)
65. M.Yu. Nalimov, Theor. Math. Phys. 80, 819 (1989)
66. M.Yu. Nalimov, Theor. Math. Phys. 102, 163 (1995)
67. A.Z. Patashinsky, V.L. Pokrovsky, Sov. Phys. JTPH 64, 1445 (1973)
68. J.-D. Fournier, P.L. Sulem, A. Pouquet, J. Phys. A 15, 1393 (1982)
69. L.Ts. Adzhemyan, A.N. Vasiliev, M. Gnatich, Theor. Math. Phys. 64, 777 (1985)
70. L.Ts. Adzhemyan, D. Volchenkov, M.Yu. Nalimov, Theor. Math. Phys. 107, 142 (1996)
71. D. Volchenkov, Phys. Lett. A 265, 122 (2000)
72. D. Volchenkov, Acta St.-Peterburg State Univ.: Phys. Chem. 2, 9 (1997)
73. D. Volchenkov, Intern. J. Mod. Phys. B 15, 1147 (2001)
74. D. Volchenkov, J. Phys.: Conf. Ser. 7, 214 (2005)
75. D. Volchenkov, B. Cessac, Ph. Blanchard, Int. J. Mod. Phys. B 16, 1171 (2002)
76. S.J. Camargo, H. Tasso, Phys. Fluids B 4, 1199 (1992)
77. M. Jurcisin, M. Stehlik, J. Phys. A: Math. Gen. 39, 8035 (2006)
78. A.E. Lifschitz, Magnetohydrodynamics and Spectral Theory (Kluwer Academic Publishers, 1989)
79. G.L. Eyink, Phys. Fluids 6, 3063 (1994)
80. L.D. Landau, E.M. Lifshitz, Hydrodynamics, Theoretical Physics, Vol. 5 (Butterworth-Heinemenn, Oxford, 1995)
81. L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemenn, Oxford, 1995)
82. D.L. Rudakov, et al., Plasma Phys.: Contr. Fusion 44, 2041 (2002)
83. B. Labombard, et al., Nucl. Fusion 40, 2041 (2000)
84. G.Y. Antar, P. Devynck, X. Garbet, S.C. Luckhardt, Phys. Plasmas 8, 1612 (2001)
85. Ph. Ghendrih, Y. Sarazin, G. Attuel, S. Benkadda, P. Beyer, G. Falchetto, C. Figarella, X. Garbet, V. Grandgirard, M. Ottaviani, Nucl. Fusion 43, 1013 (2003)
86. G. Ciraolo, Ph. Ghendrih, Y. Sarazin, C. Chandre, R. Lima, M. Vittot, M. Pettini, J. Nucl. Mater. 363-365, 550 (2007)
87. C. Chandre, M. Vittot, G. Ciraolo, Ph. Ghendrih, R. Lima, Nucl. Fusion J. Plasma Phys.: Thermonucl. Fusion 46, 33 (2006)
88. A.V. Nedospasov, et al., Sov. J. Plasma Phys. 15, 659 (1989)
89. X. Garbet, et al., Nucl. Fusion 31, 967 (1991)
90. R.Z. Sagdeev, G.M. Zaslavsky, in Nonlinear Phenomena in Plasma Physics and Hydrodynamics, edited by R.Z. Sagdeev (Mir Publishers, Moscow, 1986)
91. E. Floriani, D. Volchenkov, R. Lima, J. Phys. A 36, 4771 (2003)
92. J. Gunn, Phys. Plasmas 8, 1040 (2001)
93. P.C. Stangeby, M.C. McCracken, Nucl. Fusion 30, 1225 (1990)
94. B. Labombard, Phys. Plasmas 9, 1300 (2002)
95. B.A. Carreras, et al., Phys. Plasmas 3, 2664 (1996)
96. G. Pelletier, J. Plasma Phys. 24, 421 (1980)
97. V.E. Zaharov, Sov. Phys. JETP 62, 1745 (1972)
98. N.V. Antonov, Phys. Rev. E 60, 6691 (1999)
99. D. Volchenkov, B. Cessac, Ph. Blanchard, Int. J. Mod. Phys. B 16, 1171 (2002)
100. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)
101. Y.-C. Zhang, Phys. Rev. Lett. 63, 470 (1989)
102. P. Bak, How Nature Works (Springer-Verlag, 1996)
103. C. de Dominicis, L. Peliti, Phys. Rev. B 18, 353 (1978)
104. M.E.J. Newman, K. Sneppen, Phys. Rev. E 54, 6226 (1996)
105. K. Sneppen, M.E.J. Newman, Physica D 110, 209 (1997)
106. G.L. Eyink, A. Hussein, Physica D 223, 82 (2006)
107. H.J. Jensen, Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems, Cambridge Lect. Notes in Phys., Vol. 10 (Cambridge University Press, Cambridge, 1998)
108. D. Sornette, A. Johansen, I. Dornic, J. Phys. I (France) 5, 325 (1995)
109. F. Bagnoli, P. Palmerini, R. Rechtman, Phys. Rev. E 55, 3970 (1997)
110. L. Pietronero, A. Vespignani, S. Zapperi, Phys. Rev. Lett. 72, 1690 (1994)
111. A. Vespignani, S. Zapperi, L. Pietronero, Phys. Rev. E 51, 1711 (1995)
112. A. Corral, A. Díaz-Guilera, Phys. Rev. E 55, 2434 (1997)
113. P. Le Doussal, K.J. Wiese, Laboratoire de Physique Théorique de l'ENS: LPTENS 08/63, [arXiv:0812.1893v1] [cond-mat.dis-nn] (2008)
114. E.V. Ivashkevich, A.M. Povolotsky, A. Vespignani, S. Zapperi, Phys. Rev. E 60, 1239 (1999)
115. D. Foster, D.R. Nelson, M.J. Stephen, Phys. Rev. A 16, 732 (1977)
116. L.P. Kadanoff, S.R. Nagel, L. Wu, S. Zhu, Phys. Rev. A 39, 6524 (1989)
117. P. Grassberger, S.S. Manna, J. Phys. France 51, 1077 (1990)
118. J.L. Cardy, J. Phys. A 17, L961 (1984); Finite-size Scaling, edited by J.L. Cardy (North-Holland, New York, 1988)
119. R. Pastor-Satorras, A. Vespignani, Eur. Phys. J. B 18, 197 (2000)
120. M. De Menech, A.L. Stella, Physica A 309, 289 (2002)
121. C. Tebaldi, M. De Menech, A. Stella, Phys. Rev. Lett. 83, 3952 (1999)
122. T. Hwa, M. Kadar, Phys. Rev. Lett. 62, 1813 (1989)
123. G. Grinstein, D.-H. Lee, S. Sachdev, Phys. Rev. Lett. 64, 1927 (1990)
124. A. Díaz-Guilera, Europhys. Lett. 26, 177 (1994)
125. C.J. Pérez, A. Corral, A. Diaz-Guilera, K. Christensen, A. Arenas, Int. J. Mod. Phys. B 10, 1111 (1996)
126. B. Cessac, Ph. Blanchard, T. Krüger, Phys. Rev. E 64, 016133 (2001)
127. L. Pietronero, P. Tartagila, Y.-C. Zhang, Physica A 173, 22 (1991)
128. N.V. Antonov, A.N. Vasiliev, Sov. Phys. JETP 108, 885 (1995)
129. E. Brézin, S. Leibler, Phys. Rev. B 27, 594 (1982)
130. D. Volchenkov, R. Lima, Com. Nonlin. Sci. Numer. Simul. 13, 1329 (2008)
131. G.I. Sivashinsky, Acta Astronaut. 4, 1207 (1977)
132. L.D. Landau, Acta Phys. Chem. USSR 19, 77 (1944)
133. G. Darrieus, Presented at La Technique Moderne, Paris (1938) and at 6th Int. Cong. Appl. Mech. Paris (1946)
134. D.M. Michelson, G.I. Sivashinsky, Acta Astronaut. 4, 1207 (1977)
135. Yu.A. Gostincev, A.G. Istratov, Yu.V. Shulenin, Combust. Explos. Shock Waves 24, 70 (1989)
136. Ya.B. Zel'dovich, B. Istratov, A.G. Kidin, V.B. Librovich, Combust. Sci. Technol. 24, 1 (1980)
137. P. Pelcé, Dynamics of Curved Fronts (Academic, NY, 1989)
138. P. Pelcé, P. Clavin, Europhys. Lett. 3, 907 (1987)
139. O. Thual, U. Frish, M. Henon, J. Phys. (France) 46, 1485 (1985)
140. G. Joulin, P. Cambray, Combust. Sci. Tech. 81, 243 (1992)
141. M. Renardy, Physica D 28, 155 (1987)
142. O. Rahibe, N. Aubry, G.I. Sivashinsky. Phys. Rev. E 54, 4958 (1996)
143. O. Rahibe, N. Aubry, G.I. Sivashinsky, Combust. Theory Modeling 2, 19 (1998)
144. G. Joulin, in Combustion, Detonation, and Shock Waves, Vol. 1, edited by S.M. Frolov (Combustion Institute, Moscow, 1996)
145. D. Vaynblat, M. Matalon. SIAM J. Appl. Math. 60, 679 (2000)
146. O. Kupervasser, Z. Olami, I. Procaccia, Phys. Rev. Lett. 76, 146 (1996)
147. L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasiliev, Phys. Rev. E 58, 1823 (1998)
148. V. Gurarie, A. Migdal, Phys. Rev. E 54, 4908 (1996)
149. G. Falkovich, I. Kolokolov, V. Lebedev, A. Migdal, Phys. Rev. E 54, 4896 (1996)
150. M.Yu. Nalimov, A.A. Udalov, Acta St.-Peterburg State Univ.: Phys., Chem. 4, 33 (1996)
151. C. de Dominicis, J. Phys. C (France) 37, 201 (1976)
152. L.D. Faddeev, V.N. Popov, Phys. Lett. B 25, 29 (1967)
153. R. Courant, K. Friedrichs, H. Lewy, Math. Ann. 100, 32 (1928)
154. D.A. Batchelor, M. Beck, A. Becoulet, R.V. Budny, C.S. Chang, P.H. Diamond, J.Q. Dong, G.Y. Fu, A. Fukuyama, T.S. Hahm, D.E. Keyes, Y. Kishimoto, S. Klasky, L.L. Lao, K. Li, Z. Lin, B. Ludaescher, J. Manickam, N. Nakajima, T. Ozeki, N. Podhorszki, W.M. Tang, M.A. Vouk, R.E. Waltz, S.J. Wang, H.R. Wilson, X.Q. Xu, M. Yagi, F. Zonca, Plasma Sci. Techn. 9 (2007)
155. H.P. McKean, Comm. Pure Appl. Math. 28, 323 (1975); 29, 553 (1976)
156. E.B. Dynkin, Prob. Theory Rel. Fields 89, 89 (1991); Diffusions, Superdiffusions and Partial Differential Equations, Ams Colloquium Pubs., Providence (2002)
157. Y. LeJan, A.S. Sznitman, Prob. Theory Relat. Fields 109, 343 (1997)
158. E. Waymire, R. Bhattacharya, M. Greiner, V.K. Gupta, J.C. Ossiander, E. Thomann, B.M. Troutman, D. Winn, Lectures on Multiscale and Multiplicative Processes in Fluid Flows, Instructional and Research Workshop on Multiplicative Processes and Fluid Flows at MaPhySto, University of Aarhus (2001)
159. R.N. Bhattacharya, E.C. Waymire, Stochastic Processes with Applications (Wiley, New York, 1990)
160. Y. Le Jan, A.S. Sznitman, Probab. Theory Relat. Fields 109, 343 (1997)
161. L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasiliev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach Publ., NewYork, 1999)
162. M. Doi, J. Phys. A 9, 1465 (1976)
163. M. Doi, J. Phys. A 9, 1479 (1976)
164. Ya.B. Zel'dovich, A.A. Ovchinnikov, Sov. Phys. JTEP 74, 1588 (1978)
165. P. Grassberger, M. Scheunert, Fortschr. Phys. 28, 547 (1980)
166. L. Peliti, J. Phys. A 19, L365 (1986)
167. B.P. Lee, J. Phys. A 27, 2633 (1994)
168. J.L. Cardy, U.C. Täuber, Phys. Rev. Lett. 77, 4780 (1996)
169. J.L. Cardy, U.C. Täuber, J. Stat. Phys. 90, 1 (1998)
170. K. Symanzik, Nucl. Phys. B 190, 1 (1981)
171. N.V. Antonov, J. Honkonen, Phys. Rev. E 66, 046105 (2002)
172. M.E. Ossiander, E.C. Waymire, Ann. Stat. 28, 1 (2000)
173. V. Gurarie, A. Migdal, Phys. Rev. E 54, 4908 (1996)
174. D. Volchenkov, R. Lima, Phys. Rev. E 64, 011204 (2001)
175. A.Yu. Andreanov, M.V. Komarova, M.Yu. Nalimov, J. Phys. A 39, 7815 (2006)
176. J. Honkonen, M.V. Komarova, M.Yu. Nalimov, Nucl. Phys. B 714, 292 (2005)
177. J. Honkonen, M.V. Komarova, M.Yu. Nalimov, Nucl. Phys. B 707, 493 (2005)
178. J.C. Le Guillou, J. Zinn-Justin, Large Order Behaviour of Perturbation Theory (North-Holland, 1990)
179. J. Zinn-Justin, Ann. l'institut Fourier 53, 1259 (2003)
180. A. Kupiainen, P. Muratore-Ginanneschi, J. Stat. Phys. 126, 669 (2007)
181. E.C. Waymire, Prob. Surveys 2, 1 (2005)
182. R.N. Bhattacharya, et al., Trans. Amer. Math. Soc. 355, 5003 (2003)
183. M. Ossiander, Probab. Theory Relat. Fields 133, 267 (2005)
184. E. Nelson, Dynamical Theories of Brownian Motion (Princeton University Press, 1967)
185. E. Carlen, Conservative Diffusions: A Constructive Approach to Nelosn's Stochastic Mechanics, Ph.D. Princeton (1984)
186. E. Carlen, Comm. Math. Phys. 94, 293 (1984)
187. W.A. Zweng, Seminartingales dans les Variétés et Méchanique Stochastique de Nelson, Thèse Strasbourg (1984)
188. W.A. Zheng, Ann. Inst. H. Poincaré 21, 103 (1985)
189. D. Lind, B. Marcus, An Introduction to Symbolic Dynamics and Coding (Cambridge University Press, Cambridge, 2003)