References

1. Perrin, J.B. (1908). Comptes Rendus, Paris, 146, 967.2. Chandrasekhar, S. (1943). Reviews of Modern Physics, 15, 1.3. Bouchaud, G.P. and Gorges, A. (1990). Physics Reports, 195, 132–292.4. Haus, J.W. and Kehr, K.W. (1987). Physics Reports, 150, 263.5. Gardiner, C.W. (1985). Handbook of Stochastic Methods. Springer-Verlag, Berlin.6. Montroll, E.W. and Shlesinger, M.F. (1984). On the wonderful world of random walks, in

Studies in Statistical Mechanics 11, 1. Elsevier Science, Amsterdam.7. Montroll, E.W. and West, B.J. (1979). On an enriched collection of stochastic processes, in

Fluctuation Phenomena. Elsevier, Amsterdam.8. Mazo, R.M. (2002). Brownian Motion, Fluctuations, Dynamics and Applicatins. Clarendon

Press, Oxford.9. Berg, H.C. (1969). Random Walks in Biology. Princeton University Press, Princeton, NJ.

10. Weiss, G.H. (1994). Aspects and Applications of the Random Walk. Elsevier, Amsterdam.11. Zeldovich, Ya. B., Ruzmaikin, A.A., and Sokoloff, D.D. (1990). The Almighty Chance. World

Scientific, Singapore.12. Moffatt, H.K. (1981). Journal of Fluid Mechanics, 106, 27.13. Moffatt, H.K. (1983). Reports on Progress in Physics, 621, 3.14. Sornette, D. (2006). Critical Phenomena in Natural Sciences. Springer-Verlag, Berlin.15. Horton W. and Ichikawa, Y.-H. (1994). Chaos and Structures in Nonlinear Plasmas. World

Scientific, Singapore.16. Ben-Avraham, D. and Havlin, S. (1996). Diffusion and Reactions in Fractalsand Disordered

Systems. Cambridge University Press, Cambridge, U.K.17. Krommes, J.A. (2002). Physics Reports, 360, 1–352.18. Crisanti, A., Falcioni, M., and Vulpiani, A. (1991). Revista Del Nuovo Cimento, 14, 1–80.19. Childress, S. and Gilbert, A.D. (1995). Stretch, Twist, Fold: The Fast Dynamo. Springer-

Verlag, Berlin.20. Bakunin, O.G. (2004). Report on Progress in Physics, 67, 965.21. Csanady, G.T. (1972). Turbulent Diffusion in the Environment. D. Reidel, Dordrecht.22. Cushman-Roisin, B. (1994). Introduction to Geophysical Fluid Dynamics. Prentice-Hall,

Englewood Cliffs, NJ.23. Frenkiel, N.F., ed. (1959). Atmospheric Diffusion and Air Pollution. Academic Press,

New York.24. Nieuwstadt, F.T.M. and Van Dop, H., eds. (1981). Atmospheric Turbulence and Air Pollution

Modeling. D. Reidel, Dordrecht.25. Panofsky, H.A. and Dutton, I.A. (1970). Atmospheric Turbulence, Models and Methods for

Engineering Applications. Wiley Interscience, New York.26. Pasquill, F. and Smith, F.B. (1983). Atmospheric Diffusion. Ellis Horwood Limited, Halsted

Press, New York.

255

256 References

27. Davydov, B.I. (1934). Dokladu Akademii Nauk SSSR, 2, 474.28. Monin, A.S. and Yaglom, A.M. (1975). Statistical Fluid Mechanics. MIT Press,

Cambridge, MA.29. Cattaneo, A. (1948–1949). Attic Seminarium on Matematical Fisics University Modena,

3, 83.30. Goldstein, S. and Quart, J. (1951). Mechanics of Applied Materials, 4(4.1), 129.31. Davies, R.W. (1954). Physics Reviews, 93, 1169.32. Zel’dovich, Ya.B. and Myshkis, A.D. (1973). Principles of Mathematical Physics. Nauka,

Moscow.33. Bakunin, O.G. (2003). Physics-Uspekhi, 46, 323.34. Zaslavsky, G.M. (2002). Physics Reports, 371, 461–580.35. Pekalski, A. and Sznajd-Weron, K., eds. (1999). Anomalous Diffusion. From Basics to Ap-

plications. Springer-Verlag, Berlin.36. West, B.J., Bologna, M., and Grigolini, P. (2003). Physics of Fractal Operators. Springer-

Verlag, New York.37. Zaslavsky, G.M. (1994). Chaos, 4, 253.38. Chechkin, A.V. and Gonchar, V.Y. (2000). JETP, 91, 635.39. Bakunin, O.G. (2004). Plasma Physics Reports, 30, 303.40. Yaglom, A.M. (1981). Correlation Theory of Time-Independent Random Functions. Gosme-

teoizdat, Leningrad.41. Frost, W. and Moulden, T.H., ed. (1977). Handbook of Turbulence. Plenum Press, New York.42. Langeven, P. (1908). Comptes Rendus Paris, 146, 530.43. Taylor, G.I. (1921). Proceedings of the London Mathematical Society Series 2, 20, 196.44. Kampe de Feriet, J. (1939). Annals of the Society for Science Bruxelles, 59, 145.45. Balescu, R. (1997). Statistical Dynamics. Imperial College Press, London.46. Horton, W. (1999). Reviews of Modern Physics, 71, 735.47. Terry, P.W. (2000). Reviews of Modern Physics, 72, 109.48. Kadomtsev, B.B. (1976). Collective Phenomena in Plasma. Nauka, Moscow.49. Balescu, R. (2005). Aspects of Anomalous Transport in Plasmas. IOP, Bristol and

Philadelphia.50. Wesson, J.A. (1987). Tokamaks. Oxford University Press, Oxford.51. Pope, S.B. (1994). Annual Reviews of Fluid Mechanics, 26, 233–263.52. Sutton, O.G. (1934). Proceedings of the Royal Society A, 146, 701.53. Klyatskin, V. I. (2001). Stochastic Equations by the Physicist’s Eyes. Fizmatlit, Moscow.54. Haken, H. (1983). Advanced Synergetics. Springer-Verlag, Berlin.55. Coffey, W.T., Kalmykov, Yu.P., and Waldron, J.T. (2005). The Langevin Equation. World

Scientific, Singapore.56. Van Kampen, N.G. (1984). Stochastic Processes in Physics and Chemistry. North-Holland,

Amsterdam.57. Risken, H. (1989). The Fokker-Planck Equation. Springer-Verlag, Berlin.58. Richardson, L.F. (1926). Proceedings of the Royal Society of London Series A 110, 709.59. Barenblatt, G.I. (1994). Scaling Phenomena in Fluid Mechanics. Cambridge University

Press, Cambridge, U.K.60. Herring, J.R. and McWilliams, J.C. (1987). Lecture Notes on Turbulence. World Scientific,

Singapore.61. Pope, S.B. (2006). Turbulent Flows. Cambridge University Press, Cambridge, U.K.62. Kolmogorov, N. (1941). Dokladu Akademii Nauk SSSR, 30, 299.63. Gargett, A.E., Osborn, T.R., and Nasmyth, T.W. (1984). Journal of Fluid Mechanics, 144,

231–280.64. Frisch, U. (1995). Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press,

Cambridge, U.K.65. Tsinober, A. (2004). An Informal Introduction to Turbulence. Kluwer Academic, Dordrecht.66. Golitsyn, G.S. (2006). Selected Papers. Nauka, Moscow.67. Falgarone, E. and Passot, T., eds. (2003). Turbulence and Magnetic Fields in Astrophysics.

Springer-Verlag, Berlin.

References 257

68. Tabeling, P. and Cardoso, O. (1994). Turbulence: A Tentative Dictionary. Plenum Press,New York.

69. Davidson, P.A. (2004). Turbulence: An Introduction for Scientists and Engineers. OxfordUniversity Press, Oxford.

70. Peinke, J., Kittel, A., Barth, S., and Oberlack, M., eds. (2005). Progress in Turbulence.Springer-Verlag, Berlin.

71. Obukhov, A.M. (1941). C. R. Dokladu Akademii Nauk SSSR, 32, 19.72. Batchelor, G.K. (1952). Proceedings of the Cambridge Philosophical Society, 48, 345.73. Okubo, A. (1962). Journal of Oceanological Society. Japan, 20, 286.74. Papailiou, D.P. and Lyykoudis, P.S. (1974). Journal of Fluid Mechanics, 62, 11–31.75. Friech, U. Sulem, P., and Nelkin, M. (1978). Journal of Fluid Mechanics, 87, 719.76. Hentschel, H.G.E. and Procaccia, I. (1984). Physics Reviews A, 29, 1461.77. Sawford, B. (2001). Annual Reviews of Fluid Mechanics, 33, 289–317.78. Biferale, L. and Procaccia, I. (2005). Physics Reports, 254.79. Boffetta, G., Mazzino, A., and Vulpiani, A. (2008). Transport of inert and reactive particles:

Lagrangian statistics in turbulent flow, in Transport and Mixing in Geophysical Flows, p. 37.Springer LNP-744.

80. Sreenivasan, K.R. (1999). Reviews of Modern Physics, 71, S 383.81. Mestayer, P.G. (1982). Journal of Fluid Mechanics, 125, 475.82. Chen, S. and Kraichnan, R.H. (1998). Physics of Fluids, 68, 2867.83. Falkovich, G., Gawedzki, K., and Vergassola, M. (2001). Reviews of Modern Physics,

73, 913.84. Bohr, T., Jensen, M.H., Giovanni, P., and Vulpiani, A. (2003). Dynamical Systems Approach

to Turbulence. Cambridge University Press, Cambridge, U.K.85. Berge, P., Pomeau, Y., and Vidal, C. (1988). L’ordre dans le chaos. Hermann, Editeurs des

sciences et des arts.86. Oberlack, M. and Busse, F.H., eds. (2002). Theories of Turbulence. Springer, Vienna.87. Jovanovic, J. (2004). The Statistical Dynamics of Turbulence. Springer-Verlag, Berlin.88. Lee, J.H.W. and Chu, V.H. (2003). Turbulent Jets and Plumes—A Lagrangian Approach.

Kluwer Academic, Dordrecht.89. Einstein, A. (1905). Annalen der Physik, 17, 549.90. Haken, H. (1978). Synergetics. Springer-Verlag, Berlin.91. Isichenko, M.B. (1992). Reviews of Modern Physics, 64, 961.92. Metzler, R. and Klafter, J. (2000). Physics Reports, 339, 1.93. Kuramoto, Y. (1984). Chemical Oscillations, Waves and Turbulence. Springer-Verlag, Berlin.94. Ott, E. (1993). Chaos in Dynamical Systems. Cambridge University Press, Cambridge, U.K.95. Chate, H., Villermaux, E., and Chomaz, J.-M., eds. (1988). Mixing Chaos and Turbulence.

Kluwer Academic/Plenum Press, New York.96. Beck, C. and Schlogl, F. (1993). Thermodynamics of Chaotic Systems. Cambridge University

Press, Cambridge, U.K.97. Nicolis, J.S. (1989). Dynamics of Hierarchical Systems. An Evolution Approach. Springer-

Verlag, Berlin.98. Berdichevski, V. (1998). Thermodynamics of Chaos and Order. Longman, White Plains, NY.99. Smoluchwski, M. (1916). Physikalische Zeitschrift, 17, 557.

100. Chapman, S. (1916). Philosophical Transactions of the Royal Society, A216, 279.101. Kolmogorov, A.N. (1931). Mathematische Annalen, 104, 415.102. Shiesinger, M.F. and Zaslavsky, G.M. (1995). Levy Flights and Related Topics in Physics.

Springer-Verlag, Berlin.103. Zumofen, G., Klafter, J., and Shlesinger, M.F. (1997). Physics Reports, 290, 157.104. Khintchine, A.Ya. and Levy, P. (1936). Comptes Rendus Paris, 202, 274.105. Cauchy, A. (1853). Comptes Rendus Paris, 37, 292.106. Monin, A.S. (1955). Dokladu Akademii Nauk SSSR, 105, 256.107. Boffetta, G. and Sokolov, I.M. (2002). Physics Of Fluids, 14, 3224.108. Boffetta, G., Celani, A., Crisanti, A., and Vulpiani, A. (1999). Physics Reviews E, 60, 6734.109. Warhaft, Z. (2000). Annual Reviews of Fluid Mechanics, 32, 203–240.

258 References

110. Piquet, J. (1999). Turbulent Flows. Models and Physics. Springer-Verlag, Berlin.111. Weinstok, J. (1976). Physics of Fluids, 19, 11.112. Kreichnan, R.H. (1977). Journal of Fluid Mechanics, 81, 385.113. Kaneda, Y. and Ishida, T. (2000). Journal of Fluid Mechanics, 402, 311.114. Hay, J.S. and Pasquill, F. (1959). Advances in Geophysics, 6, 345.115. Cambon, C., Godeferd, F.S., Nicolleau, F., and Vassilicos, J.C. (2004). Journal of Fluid Me-

chanics, 499, 231.116. Kraichnan, R.H. (1970). Physics of Fluids, 13, 22.117. Koch, D.L. and Brady, J.F. (1990). Physics of Fluids A, 1, 47.118. Maurel, A. and Petitjeans, P., eds. (2000). Vortex Structure and Dynamics Workshop.

Springer-Verlag, Berlin.119. Majda, A.J. and Bertozzi, A.L. (2002). Vorticity and Incompressible Flow. Cambridge

University Press, Cambridge, U.K.120. Batchelor, G.K. (2000). Introduction to Fluid Dynamics. Cambridge University Press,

Cambridge, U.K.121. Doering, C.R. and Gibbon, J.D. (1995). Applied Analysis of the Navier-Stokes Equations.

Cambridge University Press, Cambridge, U.K.122. Aref, H. and El Naschie, M.S. (1994). Chaos Applied to Fluid Mixing. Pergamon Press,

Oxford.123. Resibois, P. and De Leener, M. (1977). Classical Kinetic Theory. John Wiley, New York.124. Berne, B.J. (1972). Chemical Physics, 56, 2164.125. Howells, I. (1960). Journal of Fluid Mechanics, 9, 104.126. Taylor, J.B. and McNamara, B. (1971). Physics of Fluids, 14, 1492.127. Dupree, T.H. (1966). Physics of Fluids, 9, 1773.128. Dupree, T.H. (1967). Physics of Fluids, 10, 1049.129. Dupree, T.H. (1972). Physics of Fluids, 15, 334.130. Balescu, R., Wang, H., and Misguich, J. (1994). Physics of Plasmas, 51, 3826.131. Taylor, G.I. (1953). Proceedings of the Royal Society of London Series A, 219, 186.132. Taylor, G.I. (1954). Proceedings of the Royal Society of London Series A, 223, 446.133. Tatarinova, E., et al. (1991). Europhysical Letters, 14, 773.134. Zel’dovich, Ya.B. (1982). Dokladu Akademii Nauk SSSR, 27, 797.135. Dreizin, Yu.A. and Dykhne, A.M. (1973). Soviet Physics JETP, 36, 127.136. Zel’dovich, Ya.B. (1937). JETP, 7, 12, 1466.137. Vedenov, A. Velikhov, E.P., and Sagdeev, R.Z. (1962). Plasma Physics and Controlled Nu-

clear Fusion Research, 2, 82.138. Drummond, W.E. and Pines, D. (1962). Plasma Physics and Controlled Nuclear Fusion Re-

search, 3, 1049.139. Dorfman, J.R. (1999). An Introduction to Chaos in Nonequilibrium Statistical Mechanics.

Cambridge University Press, Cambridge, U.K.140. Pecseli, H.L. (2006). Fluctuations in Physical Systems. Cambridge University Press,

Cambridge, U.K.141. Balescu, R. (2005). Aspects of Anomalous Transport in Plasmas. IOP, Bristol and

Philadelphia.142. Reichl, L.E. (1998). A Modern Course in Statistical Physics. Wiley-Interscience, New York.143. Joseph, D.D. and Prezioso, L. (1989). Reviews of Modern Physics, 61, 41.144. De Gennes, P.-G. (1979). Scaling Concepts in Polymer Physics. Cornell University Press,

Ithaca, NY.145. Frisch, U. (1995). Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University.

Press, Cambridge, U.K.146. Avellaneda, M. and Majda, A J. (1992). Physics of Fluids, 4, 41.147. Bakunin, O.G. (2006). Journal of Plasma Physics, 72, 647–670.148. Matheron, G. and De Marsily, G. (1980). Water Resources Research, 16, 901.149. Redner, S. (1989). Physica D, 38, 287.150. Bouchaud, J.-P. and Georges, A. (1990). Physics Review Letters, 64, 2503.

References 259

151. Scott, B. in: Dinklage, A., Klinger, T., Marx, G., and Schweikhard, L. (2005). PlasmaPhysics, Confinement, Transport and Collective Effects. Springer-Verlag, Berlin.

152. Proctor, M.R.E. and Gilbert A.D., eds. (1994). Lectures on Solar and Planetary Dynamos.Cambridge University Press, Cambridge, U.K.

153. Rosenbluth, M.N. and Sagdeev, R.Z., eds. (1984). Handbook of Plasma Physics. North-Holland, Amsterdam.

154. Brandenburg, A. (2005). Physics Reports, 417, 1.155. Jokipii, J.R. and Parker, E.N. (1969). The Astrophysical Journal, 155, 777.156. Rosenbluth, M.N., Sagdeev, R.Z., and Taylor, L.B. (1966). Nuclear Fusion, 6, 297.157. Kadomtsev, B.B. and Pogutse, O.P. (1978). Plasma Physics and Controlled Nuclear Fusion

Research, Proceedings of the 7-th International Conference, IAEA Vienna, 1, 649.158. Getmantsev, G.G. (1962). Astronomy Reports, 6, 477.159. Giacalone, J. and Jokipii, J.R. (1999). The Astrophysical Journal, 520, 204–214.160. Krommes, J.A. (1978). Progress in Theoretical Physics (Supplement), 64, 137.161. Krommes, J.A. (1983). Journal of Plasma Physics, 30, 11.162. Vainshtein, S.I. (1983). Magnetic Fields in Space. Nauka, Moscow.163. Zaslavsky, G.M. and Chirikov, B.V. (1972). Soviet Physics Uspekhi, 14, 549.164. Rechester, A.B. and Rosenbluth, M.N. (1978). Physics Reviews Letters, 40, 38.165. Ptuskin, V.S. (1979). Astrophysics and Space Science, 61, 251.166. Rechester, A.B., Rosenbluth, M.N., and White, R.B. (1979). Physics Review Letters,

42, 1247.167. Stix, T.X. (1978). Nuclear Fusion, 18, 353.168. Moffatt, H.K., Zaslavsky, G.M., Comte, P., and Tabor, M. (1992). Topological Aspects of the

Dynamics of Fluids and Plasmas. Kluwer Academic, Dordrecht..169. Barghouty, A.F. and Jokipii, J.P. (1996). The Astrophysical Journal, 470, 858–863.170. Kadomtsev, B.B. (1976). Collective Phenomena in Plasma. Nauka, Moscow.171. Kingsep, A.S. (1996). Introduction to the Nonlinear Plasma Physics. Moskovskiy Fiziko-

Tekhnichesky Institute, Moscow.172. Tsytovich, V.N. (1974). Theory of Turbulent Plasma. Plenum Press, New York.173. Chandran, B.D. and Cowley, S.C. (1998). Physics Review Letters, 80, 3077.174. Osipenko, M.V., Pogutse, O.P., and Chudin, N.V. (1987). Soviet Journal of Plasma Physics,

13, 550.175. Rosenbluth, M.N., Berk, H.L. Doxoas, I., and Horton, W. (1987). Physics of Fluids, 30, 2636.176. Solomon, T. and Gollub, J. (1988). Physics Reviews A, 38, 6280.177. Solomon, T. and Gollub, J. (1988). Physics of Fluids A, 31, 1372.178. Squires, T. and Quake, S. (2005). Reviews of Modern Physics, 77, 986.179. Ziman, J.M. (1979). Models of Disorder: The Theoretical Physics of Homogeneously Disor-

dered Systems. Cambridge University Press, London.180. Tabeling, P. (2002). Physics Reports, 362, 1–62.181. Stolovitzky, G. and Sreenivasan, K.R. (1994). Reviews of Modern Physics, 66, 229.182. Batchelor, G.K., Moffat, H.K., and Worster, M.G. (2000). Perspectives in Fluid Dynamics.

Cambridge University Press, Cambridge, U.K.183. Holmes, P.J., Lumley, J.L., Berkooz, G., Mattingly, J.C., and Wittenberg, R.W. (1997).

Physics Reports, 326, 337–384.184. Kraichnan, R.H. and Montgomery, D. (1980). Reports on Progress in Physics, 43, 547.185. Pismen, L.M. (2006). Patterns and Interfaces in Dissipative Dynamics. Springer-Verlag,

Berlin.186. Bohm, D. and Burhop, E. (1949). Electric Discharge, Princeton University Press, New York.187. Golitsyn, G.S. (1980). Dokladu Akademii Nauk SSSR, 251, N6 284.188. Mandelbrot, B.B. (1977). Fractals: Form, Chance, and Dimension. W.H. Freeman, San

Francisco.189. Feder, J. (1988). Fractals. Plenum Press, New York.190. Bunde, A. and Havlin, S., eds. (1996). Fractals in Science. Springer-Verlag, Berlin.191. Bunde, A. and Havlin, S., eds. (1995). Fractals and Disordered Systems. Springer-Verlag,

Berlin.

260 References

192. Chorin, A.J. (1994). Vorticity and Turbulence. Springer-Verlag, New York.193. Gouyet, J.-F. (1996). Physics and Fractal Structure. Springer-Verlag, Berlin.194. Guyon, E., Nadal, J.-P., and Pomeau, Y., eds. (1988). Disorder and Mixing. Kluwer Aca-

demic, Dordrecht.195. Pietronero, L. (1988). Fractals’ Physical Origin and Properties. Plenum Press, New York.196. Schroeder, M. (2001). Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise. W.H.

Freeman, New York.197. Schweitzer, F. (2003). Brownian Agents and Active Particles. Springer-Verlag, Berlin.198. Lovejoy, S. (1982). Science, 216, 185.199. Mandelbrot, B.B. (1975). Journal of Fluid Mechanics, 72, 401.200. Broadbent, S.R. and Hammersley, J.M. (1957). Proceedings of the Cambridge Philosophical

Society, 53, 629.201. Stauffer, D. (1985). Introduction to Percolation Theory. Taylor and Francis, London.202. Stanley, H.E. (1984). Journal of Statistical Physics, 34, 843.203. Sokolov, I.M. (1986). Soviet Physics Uspekhi, 29, 924.204. Stauffer, D. (1979). Physics Reports, 2, 3.205. Stanley, H.E. (1971). Introduction to Phase Transitions and Critical Phenomena. Clarendon

Press, Oxford.206. Bunde, A. and Gouet, J.F. (1985). Journal of Physics A, 18, L285.207. Saleur, H. and Duplantier, B. (1987). Physics Review Letters, 58, 2325.208. Sapoval, B., Rosso, B., and Gouyet, J. (1985). Journal of Physics Letters, 46, 149.209. Levinshtein, M.E., Shklovsky, B.I., Shur, M.S., and Efros, A.L. (1976). JETP, 42, 112.210. Hunt, A. (2005). Percolation Theory for Flow in Porous Media. Springer-Verlag, Berlin

(LNP-674).211. Sahimi, M. (1993). Application of Percolation Theory. Taylor and Francis, London.212. Halperin, B.I., Feng, S., and Sen, P.N. (1985). Physics Review Letters, 54, 2891.213. Feng, S., Halperin, B.I., and Sen, P.N. (1987). Physics Reviews B, 35, 197.214. Trugman, S.A. (1983). Physics Reviews B, 27, 7539.215. Fanjiang, A. (1997). Journal of Statistical Physics, 88, 1033.216. Isichenko, M.B., Kalda, Ya.L, Tatarinova, E.V., Telkovskaya, O.V., and Yankov, V.V. (1989).

Soviet Physics JETP, 69, 517.217. Gruzinov, A.V., Isichenko, M.B., and Kalda, Ya.L. (1990). Soviet Physics JETP, 70, 263.218. Danilov, S.D., Dovgenko, V.A., and Yakushkin, I.G. (2000). JETP, 118, 483–494.219. Reuss, J.-D. and Misguich, J.H. (1996). Physics Reviews E, 54, 1857.220. Reuss, J.-D., Spineanu, F., and Misguich, J.H. (1998). Journal of Plasma Physics, 59, 707.221. Silva, L.O. (2006). Astrophysics Journal Letters, 596, L121.222. Yushmanov, P.N. (1992). Plasma Physics and Controlled Fusion, 14, 313.223. Smolyakov, A.I. and Yushmanov, P.N. (1993). Nuclear Fusion, 3, 383.224. Bakunin, O.G. (2003). Plasma Physics and Controlled Nuclear Fusion, 45, 1909.225. Bakunin, O.G. (2005). Physica A, 351, 241.226. Bakunin, O.G. (2005). Journal of Plasma Physics, 71, 435.227. Isichenko, M.B., Horton, W., Kim, D.E., Heo, E.G., and Choi, D.-I. (1992). Physics of Fluids,

4, 3973.228. Zimbardo, G., Veltri, P., and Pommois, P. (2000). Physics Reviews E, 61, 1940.229. Bickertom, R.J. (1997). Plasma Physics and Controlled Fusion, 39, 339.230. Isichenko, M.B. (1991). Plasma Physics and Controlled Fusion, 33, 795.231. Isichenko, M.B. (1991). Plasma Physics and Controlled Fusion, 33, 809.232. Ottaviani, M. (1992). Europhysical Letters, 20, 111.233. Isichenko, M.B. and Kalda, J. (1991). Journal of Nonlinear Science, 1, 255.234. Isichenko, M.B. and Kalda, J. (1991). Journal of Nonlinear Science, 1, 375.235. Mitsugu, M., Ouchi, S., and Honda, K. (1991). Journal of the Physics Society of Japan,

60, 2109.236. Isogami, S. and Matsushita, M. (1992). Journal of the Physics Society of Japan, 61, 1445.237. Kondev, J. and Henley, C.L. (1995). Physics Review Letters, 74, 4580.238. Kondev, J., Henley, C.L., and Salinas, D.G. (2000). Physics Reviews E, 61, 104.

References 261

239. Kondev, J. (2001). Physics Review Letters, 86, 5890.240. Kalda, J. (2001). Physics Review E, 64, 020101(R).241. Kalda, J. (2003). Physics Review Letters, 90, 118501-1.242. Bakunin, O.G. and Schep, T.J. (2004). Physics Letters A, 322, 105.243. Bakunin, O.G. (2005). Chaos Solitons and Fractals, 23, 1703.244. Bakunin, O.G. (2005). Plasma Physics and Controlled Nuclear Fusion, 47, 1857.245. Iroscnikov, P.S. (1963). Astronomical Journal, 40, 742.246. Kraichnan, R.H. (1965). Physics of Fluids, 8, 1385.247. Goldreich, P. and Sridhar, S. (1997). Astrophysical Journal, 485, 680.248. Narayan, R. (1999). Physics Review Letters, 42, 1247.249. Balagurov, B.Ya. and Vaks, V.G. (1974). Soviet Physics JETP, 38, 968.250. Donsker, M. and Varadhan, S. (1979). Communications in Pure and Applied Mathematics,

32, 721.251. Kravtsov, V.E., Lerner, I.V., and Yudson, V.I. (1986). Soviet Physics JETP, 64, 336.252. Bakunin, O.G. (2003). Plasma Physics Reports, 29, 955.253. Bourdelle, C. (2005). Plasma Physics and Controlled Nuclear Fusion, 47, A317.254. Shivamoggi, B.K. (1998). Annals of Physics, 270, 263.255. Bakunin, O.G. (2004). Physica A, 347, 289.256. Bakunin, O.G. (2005). Physica A, 345, 1.257. Fradkin, L. (1991). Plasma Physics and Controlled Nuclear Fusion, 33, 685.258. Zel’dovich, Ya.B., Molchanov, S.A., Ruzmaikin, A.A., and Sokolov, D.D. (1987). Soviet

Physics Uspekhi, 30, 353.259. Balescu, R. (2000). Plasma Physics and Controlled Nuclear Fusion, 42, B1.260. Balescu, R. (1995). Physics Reviews E, 51, 4807.261. Lubashevskiy, I.A. and Zemlianov, V.E./JETP (1998). 114, 1284.262. Bakunin, O.G. (2003). Physics-Uspekhi, 46, 826.263. Montroll, E. and Weiss, G. (1965). Journal of Mathematical Physics, 6, 178.264. Montroll, E. and Scher, H. (1972). Physics Reviews Series B, 12, 2455.265. Compte, A. and Camacho, J. (1997). Physics Reviews E, 56, 5445.266. Shlesinger, M.F., Zaslavsky, G.M., and Klafter, J. (1993). Nature, 363, 31.267. Shlesinger, M.F., West, B.J., and Klafter, J. (1987). Physics Reviews Letters, 58, 1100.268. Zumofen, G., Blumen, A., Klafter, J., and Shlesinger, M.F. (1989). Journal of Statistical

Physics, 54, 1519.269. Chukbar, K. (1996). Soviet Physics JETP, 82, 719.270. Bakunin, O.G. (2004). Physica A, 337, 27.271. Bakunin, O.G. (2005). Physica A, 348, 245.272. Cardoso, O. and Tabeling, P. (1989). European Journal of Mechanics B/Fluids, 8, 459.273. Cardoso, O. and Tabeling, P. (1988). Europhysical Letters, 7, 225.274. Nezlin, M.B. (1981). JETP Letters, 34 83.275. Antipov, S.B., Nezlin, M.B., Snegkin, E.H., and Trubnikov, A.S. (1985). JETP, 89, 1905.276. Solomon, T.H., Weeks, E., and Swinney, H.L. (1994). Physica D, 76, 70.277. Weeks, E.R., Urbach, J.S., and Swinney, H.L. (1996). Physica D, 97, 291.278. Kramers, H. (1940). Physica, 7, 284.279. Hanggi, P. and Thomas, H. (1982). Physics Reports, 88, 207.280. Hanggi, P., Borkovec, M., and Talkner, P. (1990). Reviews of Modern Physics, 62, 251.281. Malchow, H. and Schimansky-Geier, L. (1985). Noise and Diffusion in Bistable Nonequilib-

rium Systems. Teuber, Leipzig.282. Hanggi, P. and Talkner, P., eds. (1995). New Trends in Kramer’s Reaction Rate Theory.

Kluwer Academic, Boston.283. Davies, R.W. (1954). Physics Reviews, 93, 1169.284. Bakunin, O.G. and Krasheninnikov, S.I. (1995). Plasma Physics Reports, 21, 502.285. Bakunin, O.G. and Krasheninnikov, S.I. (1990). Plasma Physics Reports, 16, 501.286. Bakunin, O.G. (2003). Plasma Physics Reports, 29, 785.287. Zaslavsky, G.M. and Edelman, M. (2000). Chaos, 10, 135.288. Karney, C.F. (1983). Physica D, 8, 360.

262 References

289. Bakunin, O.G. (2005). Physica A, 346, 284.290. Bakunin, O.G. (2004). Physics Letters A, 330, 23.291. Vlad, M., Spineanu, F., Misguich, J.H., and Balescu, R. (1998). Physics Reviews E, 58, 7359.292. Vlad, M., Spineanu, F., Misguich, J.H., and Balescu, R. (2002). Physics Reviews E, 66

038302.293. Vlad, M., Spineanu, F., Misguich, J.H., and Balescu, R. (2001). Physics Reviews E, 63

066304.

Index

Advection, 27, 34–36, 75–77Advection-diffusion equation, 34–36Advection subrange, 35Alfven, 205–208Alfven’s turbulence, 207–208Anisotropy, 7, 92, 200, 220, 234, 237Anomalous diffusion, 7, 47–51, 53, 60–62, 92,

98, 110–111, 147, 151, 214, 221–222,223, 238, 247–249

Atmosphere, 22, 24, 75

Batchelor, 32, 33, 34, 38, 51, 52Blasius, 27Bohm, 139, 141, 217Bohm scaling, 138–141, 217Boltzmann, 3Boundary-layer theory, 27Braded magnetic fields, 10Broadbent, 157Brown, 3, 197Brownian landscape, 196–199Brownian motion, 3–7, 47, 93, 197, 229

Cantordust, 147, 148set, 147, 149–150

Cascade phenomenology, 34–38Chapman, 43, 225, 226Continuous time random walk, 223–241comb structures, 218–220Complex structures, 10, 77, 135–136, 140Complex systems, 87, 118, 131, 221, 230, 246Convective cells, 10, 66, 115, 131–143, 170,

172, 190Correlation length, 6, 13, 18, 77, 92, 108–109,

111–114, 120, 122, 124, 126, 127, 140,

151, 157–158, 162, 163–164, 172, 174,179, 190, 207, 217, 218, 221

Correlation mechanisms, 10, 108, 117,118, 190

Correlation scale, 3–18, 62, 63, 65, 69, 77,108, 109, 122, 126, 127, 139–140, 165,169, 171–173, 175, 177, 180–181, 183,185, 188, 191, 193, 206–208, 215–216,220–221

Correlation time, 6, 11, 16–18, 23, 64–65, 77,88, 96, 109, 112, 122, 124–126, 131,133–134, 139–142, 151, 162, 169, 173,174, 178, 182, 184–185, 190, 202, 214,216–217

Corrsinconjecture, 58–59, 60–62, 66, 218, 222,

252–254independence hypothesis, 57–69

Critical exponent, 157, 158, 165

Davydov, 11Diffusion

coefficient, 5–8, 13, 16–18, 21, 24, 31–33,42, 44, 57–58, 63–67, 71, 74, 76–77, 79,81, 83, 87, 90–91, 105, 107–109, 111,114–115, 121–122, 124–127, 132, 133,135, 139–140, 142, 151, 162, 164–165,169, 174–175, 178–182, 183, 184–186,189–191, 201–202, 207, 213–214,217–219, 221, 229, 233, 235, 237, 245,247, 253–254

equation, 8–13, 18, 26, 33–35, 38, 41–53,58, 71–86, 104, 201, 235, 243–245

Diffusive motion, 3, 117, 213Dissipation range, 29Dissipation rate, 27–28, 34–35, 38, 51, 154,

156, 205–206

263

264 Index

Double diffusion, 112, 117, 124–125, 200,214–215, 220–222, 233–234, 235

Einstein, 14, 41, 43, 44, 51, 223, 226–227Energy-containing scales, 28Energy spectrum, 30–31, 36–37, 58, 64,

155–156, 204, 232Ensemble, 63, 81, 94, 98, 106, 218, 252Escape probability, 213–222, 239, 246, 248Euclidean dimension, 148Eulerian correlation, 59, 60–61, 237

Fick law, 8Field-line random walk, 107Fluctuation-dissipative relation, 136–138Fluctuations, 10, 13, 15, 34, 82, 90–91,

101–102, 106, 108–109, 136, 138–142,185–186

Fluid turbulence, 104, 129Flux-gradient relation, 11Fractal, 34, 47, 48, 50, 99, 136, 147–166,

171–172, 182–183, 190, 196–198,214–216, 232, 251

Fractal dimension, 147–151, 152, 153–154,156, 158–159, 166, 197–198, 232

Fractional derivatives, 13, 47–51, 52Fractional differential equation, 220, 226–228,

230–231, 234–236Fully developed turbulence, 38

Gaussian distribution, 9, 45, 52–53, 58, 62, 220Graded percolation, 165–166, 194, 198, 199

Hamiltonian function, 161, 246, 253Hammersley, 157Hausdorff dimension, 148Hierarchy of scales, 33, 128, 172–173,

178–181, 183–184, 193–195,203–204, 207

Howells, 64–65, 66–68, 79, 115, 237Hurst exponent, 7, 22–23, 46, 61–62, 89–91,

96–98, 112, 152, 196–197, 200,202–203, 216, 230, 233–234, 238, 239,247, 248

Inertial range, 28, 30, 36, 38, 47Ingenhousz, 3Intermittency, 34, 154, 232Internal-convective subrange, 35Isotropic turbulence, 22, 31, 51, 54, 153–154,

194, 204

Kinetic equation, 13, 243–244, 246Kohlrausch, 214, 224, 248–249

Kohlrausch relaxation function, 224Kolmogorov, 204–205, 225–226, 232Kolmogorov microscale, 36Kolmogorov phenomenology, 137, 204–205Kolmogorov spectrum, 38Kraichnan, 58, 205Kramers, 243–244Kubo number, 77–80, 110, 119, 121–122,

125, 139, 141, 175, 177, 188–189, 203,217–218, 253–254

Lagrangian correlation, 15–18, 21, 23, 57–59,61, 64, 68, 229–230, 247–248

Lagrangian correlation functions, 21, 58, 68Lagrangian description, 13–18Lagrangian particle, 13–15, 17–18Lagrangian statistics, 33Lagrangian velocity, 14, 22, 59Langevin, 14, 21, 229Levy, 34, 41, 45, 50, 53, 248, 249Levy flight, 46, 53, 221Levy-Khintchine distribution, 41Levy-stable distribution, 44–46Levy walk, 34, 231Liouville derivatives, 48Longitudinal correlations, 235–238Long-range correlations, 48, 62, 83–84, 110,

157, 169, 189Long tails, 63Lyapunov’s exponent, 118

Magnetic diffusion coefficient, 105, 107–108,111, 114–115, 122, 221

Magnetohydrodynamics, 106, 129, 204–208Magnetohydrodynamic turbulence, 129,

204–208Mandelbrot, 147, 150, 155, 202Markovian processes, 227Mean displacement, 4, 94, 247Memory effects, 12–13, 38, 44, 48, 75, 223,

225–227, 230–231, 233, 243, 251Moffat, 64, 68Molecular diffusivity, 18, 34Monin, 51–53, 231

Navier-Stokes, 26–27, 38Nested hierarchy, 193–195Newtonian fluid, 26–27Nondiffusive kinetic effects, 246Nonlocal effects, 41–53

Obukhov, 26, 30, 31, 33, 35–36, 156One-flight model, 247–249Organized structures, 129

Index 265

Passive scalar transport, 10, 109, 113Peclet number, 64–66, 73, 74, 76, 132–143,

136–138, 170–172, 175Percolation regime, 124, 172, 175, 178, 215Percolation threshold, 158, 160–163, 165Percolation transition, 157–160Percolation transport, 95, 180, 184, 186,

200, 204Perrin, 3Phase space, 81, 214, 218, 222, 243–254Phase transition, 157, 172, 247Plasma, 81, 101–108, 111, 117, 119, 123, 127,

129, 131, 138–141, 143, 204, 205, 208,221, 246, 249

Plasma turbulence, 104, 106, 139, 246Poiseuille flow, 71Poisson distribution, 213, 223, 226–227Prandtl number, 36

Random walks, 3–18, 24, 87–89, 99, 107,108, 111–112, 120, 122, 151–152, 156,196–197, 215, 223–241

Rayleigh-Benard convective rolls, 134Reconnection of streamlines, 7Relative diffusion, 23, 31–33, 41, 52, 231, 245Renormalization, 57–69, 74–76, 90, 92,

112–115, 141–143, 162–165, 169–172,175–177, 179, 182–185, 187–189,190–191, 194, 206, 214, 219, 226, 233,235–236

Return effects, 87–99Reynolds number, 27, 28, 30, 33, 36, 65,

104–106, 137Richardson, 23–26, 31–34, 51–52, 156,

231–232, 245Root-mean-square displacement, 3, 5, 6, 88

Scalar spectrum, 34–38Seed diffusion, 7, 57, 68, 75, 81, 90, 122, 132,

178, 213, 235Self-avoiding random walks, 89, 152, 156, 197Self-similar, 52–53, 147–151, 158, 196Shear flow, 37, 62, 71, 75, 87–98, 125, 165,

200–201, 235, 237–238Sierpinski carpet, 158, 159Smoluchowski, 43, 51, 223, 225–226Sticky island, 246

Sticky island boundary, 246Stochastic instability, 7, 112, 117–129, 178,

187–189, 203–204Stochastic instability increment, 119–122,

187–189, 203Stochastic magnetic field, 68, 101, 104,

106–112, 117, 119, 122, 124, 127–128,189–191, 206–208, 220–221, 233–235

Strong turbulence, 18, 137–138, 215, 217–218Subdiffusion, 161, 213–222Superdiffusion, 7, 90–92, 96–97, 202Suprathermal particles, 246System of zonal flows, 10

Taylor, 14–16, 21–22, 26, 57, 66, 68, 71–77,81, 83–84, 92, 109, 142, 229, 237, 247

Taylor dispersion, 71–75, 237Telegraph equation, 11–13, 42, 44, 52, 84–86,

226, 245Temperature spectrum, 36Transport models, 7, 180, 218–220Transverse correlations, 112, 115Trapping, 213–222, 223, 238–239, 246,

249–250, 252–253Turbulent diffusion, 6–7, 11–13, 15–18, 21–38,

44, 51, 53, 57, 64–65, 77, 92, 101, 107,109, 114, 117, 122, 131–135, 138, 142,160, 164, 166, 169, 175–176, 180–181,203, 216, 229, 233, 247, 253

Turbulent mixing, 11, 24, 136–137, 140, 208Turbulent transport, 7, 13, 16, 18, 21, 23, 32,

38, 51, 58, 62, 64, 66, 68, 74, 77, 80, 81,84, 95–98, 101, 104, 106, 107, 115, 122,138, 151, 153, 169–191, 196, 205, 208,228, 239, 245, 255

Velocity distribution, 93, 98, 245, 249–252Velocity fluctuations, 11, 13, 15, 136Velocity spectrum, 37Viscous-convective subrange, 37–38Vlasov equation, 102–103Vortex structures, 213, 238–240, 254

Waiting time distribution, 228–230, 238Well-developed turbulence, 26Wiener process, 47

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