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Reviews of topical problems


Coherent phenomena in stochastic dynamical systems

 a,  b
a A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
b Department of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

Basic ideas of the statistical topography of random processes and fields are presented, which are used in the analysis of coherent phenomena in simple dynamical systems. Such phenomena take place with probability one, and provide links between individual realizations and statistical characteristics of systems at large. We confine ourselves to several examples: transfer phenomena in singular dynamic systems under the action of random forces; dynamic localization of plane waves in randomly stratified media; clustering of randomly advected passive tracers; and formation of caustic structures for wave fields in randomly inhomogeneous media. All these phenomena are studied based on the analysis of one-point (space-time) probability distribution functions.

Fulltext pdf (584 KB)
Fulltext is also available at DOI: 10.1070/pu1999v042n02ABEH000522
PACS: 02.50.−r, 05.40.-j, 05.45.+b, 42.50.−p (all)
DOI: 10.1070/pu1999v042n02ABEH000522
URL: https://ufn.ru/en/articles/1999/2/c/
000079341200003
Citation: Klyatskin V I, Gurarie D "Coherent phenomena in stochastic dynamical systems" Phys. Usp. 42 165 (1999)
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Оригинал: Кляцкин В И, Гурарий Д «Когерентные явления в стохастических динамических системах» УФН 169 171–207 (1999); DOI: 10.3367/UFNr.0169.199902c.0171

References (69) ↓ Cited by (27) Similar articles (20)

  1. Klyatskin V I Usp. Fiz. Nauk 164 531 (1994) [Phys. Usp. 37 501 (1994)]
  2. Klyatskin V I, Saichev A I Zh. Eksp. Teor. Fiz. 111 1297 (1997) [JETP 84 716 (1997)]
  3. Klyatskin V I Statisticheskoe Opisanie Dinamicheskikh Sistem s Fluktuiruyushchimi Parametrami (Statistical Description of Dynamical Systems with Fluctuating Parameters, Moscow: Nauka, 1975)
  4. Gurbatov S N, Malakhov A N, Saichev A I Nelineînye Sluchaînye Volny v Sredakh bez Dispersiî (Moscow: Nauka, 1990) [Translated into English Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays and Particles (Manchester: Manchester University Press, 1991)]
  5. Klyatskin V I Stokhasticheskie Uravneniya i Volny v Sluchaîno-Neodnorodnykh Sredeakh (Stochastic Equations and Waves in Randomly Inhomogeneous Medium, Moscow: Nauka, 1980); Ondes et Equations Stochastiques Dans les Milieux Aliatoirement non Homogenes (Besancon Cedex, France: Les Editions de Physique, 1985)
  6. Kulkarny V A, White B S Phys. Fluids 25 1770 (1982)
  7. White B S SIAM J. Appl. Math. 44 127 (1983)
  8. Zwillinger D, White B S Wave Motion 7 207 (1985)
  9. Klyatskin V I Waves Random Media 3 93 (1993)
  10. Klyatskin V I Metod Pogruzheniya v Teorii Rasprostraneniya Voln (The Imbedding Method in Wave Propagation Theory, Moscow: Nauka,1986)
  11. Scattering and Localization of Classical Waves in Random Media (World Scientific Series on Directions in Condensed Matter Physics, Vol. 8, Ed. P Sheng, Singapore: World Scientific, 1990)
  12. Klyatskin V I, Saichev A I Usp. Fiz. Nauk 162 161 (1992) [Sov. Phys. Usp. 35 231 (1992)]
  13. Klyatskin V I, in Progress in Optics Vol. 33 (Ed. E Wolf, Amsterdam: North-Holland, 1994) p. 1
  14. Nicolis G, Prigogine I Exploring Complexity: an Introduction (New York: W.H. Freeman, 1989)
  15. Ziman J M Models of Disorder. The Theoretical Physics of Homogeneously Disordered Systems (Cambridge: Cambridge Univ. Press, 1979) [Translated into Russian (Moscow: Mir, 1982)]
  16. Kac M Bull. Amer. Math. Soc. 49 314 (1943)
  17. Rice S O Bell Syst. Tech. J. 23 282 (1944), 24 46 (1945), in Selected Papers on Noise and Stochastic Processes (Ed. N Wax, New York: Dover, 1954)
  18. Longuet-Higgins M S Proc. Cambridge Philos. Soc. 52 234 (1956), 53 230 (1957); Philos. Trans. R. Soc. London Ser. A 249 321 (1957), 250 157 (1957)
  19. Swerling P I.R.E. Tranc. Inf. Theory IT-8 315 (1962)
  20. Isichenko M B Rev. Mod. Phys. 64 961 (1992)
  21. Klyatskin V I, Woyczynski W A, in Stochastic Models in Geosystems (The IMA Volumes in Mathematics and Its Applications, Vol. 85, Eds S A Molchanov, W A Woyczynski, New York: Springer, 1997) p. 171
  22. Saichev A I, Woyczynski W A, in Stochastic Models in Geosystems (The IMA Volumes in Mathematics and Its Applications, Vol. 85, Eds S A Molchanov, W A Woyczynski, New York: Springer, 1997) p. 359
  23. Klyatskin V I, Woyczynski W A, Gurarie D, in Stochastic Modelling in Physical Oceanography (Progress in Probability, Vol. 39, Eds R J Adler, P Muller, B Rozovskii, Boston: Birkhauser, 1996) p. 221; J. Stat. Phys. 84 797 (1996)
  24. Klyatskin V I, Yakushkin I G Zh. Eksp. Teor. Fiz. 111 2044 (1997) [JETP 84 1114 (1997)]
  25. Zirbel C L, Çinlar E, in Stochastic Models in Geosystems (The IMA Volumes in Mathematics and Its Applications, Vol. 85, Eds S A Molchanov, W A Woyczynski, New York: Springer, 1997) p. 459
  26. Mesinger F J. Atmos. Sci. 22 479 (1965)
  27. Mesinger F, Mintz Y Tech. Rep. 4, 5 (Los Angeles: Dep. Meteorology, Univ. of California, 1970)
  28. Gardiner C W Handbook of Stochastik Methods for Physics, Chemistry and the Natural Sciences (Berlin: Springer-Verlag, 1985) [Translated into Russian (Moscow: Mir, 1986)]
  29. Yaroshchuk I O "Chislennoe Modelirovanie Pasprostraniniya Ploskich Voln v Sluchaino Sloistich Lineinich i Nelineinich Sredach" ("Numerical Modeling of the Propagation of Plane Waves in Randomly Layered Linear and Nonlinear Media") Ph.D dissertation (Vladivostok: Pacific Oceanological Institute, 1986)
  30. Casti J, Kalaba R Imbedding Methods in Applied Mathematics (Reading, MA: Addison-Wesley Publ. Co., 1973)
  31. Bellman R, Wing G M An Introduction to Invariant Imbedding (Philadelphia: SIAM, 1992)
  32. Kagiwada H H, Kalaba R Integral Equations Via Imbedding Methods (Reading, MA: Addison Wesley Publ. Co., 1974)
  33. Guzev M A, Klyatskin V I, Popov G I Waves Random Media 2 117 (1992)
  34. Pedlosky J Geophysical Fluid Dynamics (New York: Springer-Verlag, 1982) [Translated into Russian (Moscow: Mir, 1984)]
  35. Klyatskin V I Izv. RAN, Fiz. Atm. i Okeana 32 824 (1996) [Izv., Atmospheric Oceanic Phys. 32 757 (1996)]
  36. Klyatskin V I, Gurarie D, in Stochastic Modelling in Physical Oceanography (Progress in Probability, Vol. 39, Eds R J Adler, P Muller, B Rozovskii, Boston: Birkhauser, 1996) p. 149
  37. Gryanik N V, Klyatskin V I Izv. RAN, Fiz. Atm. i Okeana 33 723 (1997) [Izv., Atmospheric Oceanic Phys. 33 (1997)]; Graynik N V, Klyatskin V I, Gurarie D Wave Motion 28 333 (1998)
  38. Graynik N V, Klyatskin V I Zh. Eksp. Teor. Fiz. 111 2030 (1997) [JETP 84 1106 (1997)]
  39. Monin A S, Yaglom A M Statisticheskaya Gidrodinamika Ch. 1, 2 (Moscow: Nauka, 1965, 1967) [Translated into English Statistical Fluid Mechanics; Mechanics of Turbulence Vol. 1, 2 (Cambridge, Mass.: MIT Press, 1971 - 1975)]
  40. Tatarskiî V I Rasprostranenie Voln v Turbulentnoî Atmosfere (Moscow: Nauka, 1967) [Translated into English The Effects of the Turbulent Atmosphere on Wave Propagation (Springfield, Va.: National Technical Information Service, 1977)]
  41. Rytov S M, Kravtsov Yu A, Tatarskiî V I Vvedenie v Statisticheskuyu Radiofiziku Ch. 2 (Moscow: Nauka, 1978) [Translated into English Principles of Statistical Radiophysics Vol. 34 (Berlin: Springer-Verlag, 1988 - 1989)]
  42. Guzev M A, Klyatskin V I Waves Random Media 1 275 (1991)
  43. Gurvich A S, Kallistratova M A, Martvel’ F E Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20 1020 (1977) [Radiophys. Quantum Electron.20 705 (1977)]
  44. Flatté S M, Wang G-Y, Martin J J. Opt. Soc. Am. A 10 2363 (1993)
  45. Flatté S M, Bracher C, Wang G-Y J. Opt. Soc. Am. A 11 2080 (1994)
  46. Whitham G B Linear and Nonlinear Waves (New York: John Wiley & Sons Inc., 1974) [Translated into Russian (Moscow: Mir, 1977)]
  47. Landau L D, Lifshits E M Gidrodinamika (Moscow: Nauka, 1986) [Translation into English Fluid Mechanics, 2nd ed. (London: Pergamon Press, 1987)]
  48. Hopf E J. Ration. Mech. Anal. 1 87 (1952)
  49. Furutsu K J J. Res. NBS D 667 303 (1963)
  50. Novikov E A Zh. Eksp. Teor. Phys. 47 1919 (1964) [Sov. Phys. JETP 20 1290 (1965)]
  51. Donsker MD Proc. Conference on Theory and Applications of Analysis in Functional Space (Boston MA: M.I.T. Press, 1964) p. 17 [Matematika 11 128 (1967)]
  52. Klyatskin V I, in Mathematics of Random Media (Lectures in Appl. Math., Vol. 27, Eds W E Kohler, B S White, Providence, R.I.: AMS, 1991) p. 447
  53. Lifshits I M, Gredeskul S A, Pastur L A Vvedenie v Teoriyu Neuporyadochennyk Sistem (Moscow: Nauka, 1982) [Translation into English Introduction to the Theory of Disordered Systems (New York: Wiley, 1988)]
  54. Anzygina T N, Pastur L A, Slyusarev V A Fizika Nizkikh temper. 7 5 (1981) [Sov. J. Low Temp. Phys. 7 1 (1981)]
  55. Klyatskin V I, Woyczynski W A Zh. Eksp. Teor. Fiz. 108 1403 (1995) [JETP 81 770 (1995)]
  56. Pumir A, Shraiman B, Siggia E D Phys. Rev. Lett. 66 2984 (1991)
  57. Gollub J P et al. Phys. Rev. Lett. 67 3507 (1991)
  58. Holzer M, Pumir A Phys. Rev. E 47 202 (1993)
  59. Pumir A Phys. Fluids 6 2118 (1994)
  60. Holzer M, Siggia E D Phys. Fluids 6 1820 (1994)
  61. Kerstein A R, McMurtry P A Phys. Rev. E 49 474 (1994)
  62. Shraiman B I, Siggia E D Phys. Rev. E 49 2912 (1994)
  63. Klyatskin V I, Nalbandyan O G Izv. RAN, Fiz. Atm. i Okeana 32 291 (1997) [Izv. Atmospheric Oceanic Phys. 32 (1997)]
  64. Bunkin F V, Gochelashvili K S Izv. Vyssh. Uchebn. Radiofiz. 11 1864 (1968) [Radiophys. Quantum Electron. 11 1059 (1968)]
  65. Bunkin F V, Gochelashvili K S Izv. Vyssh. Uchebn. Radiofiz. 12 875 (1969)[Radiophys. Quantum Electron. 12 697 (1969)]
  66. Gochelashvili K S, Shishov V I Volny v Sluchaîno-Neodnorodnykh Sredakh (Waves in Randomly Inhomogeneous Media, Itogi Nauki i Tekhniki. Ser. Radiofizika. Fizicheskie Osnovy Elektroniki. Akustika, Vol. 1, Ed. N D Ustinov, Moscow: Izd. VINITI AN SSSR, 1981)
  67. Dashen R Opt. Lett. 9 110 (1984)
  68. Churnside J H, Clifford S F J. Opt. Soc. Am. A 4 1923 (1987)
  69. Yakushkin I G, Zavorotny V U Waves Random Media 2 165 (1992)
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