RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2016

 / 

January

←  →

Physics of our days


Stochastic structure formation in random media


A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation

Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case spatial structures (clusters) may form with probability one in almost every system realization due to rare events happening with vanishing probability. The problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, physics of plasma, astrophysics and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (the rogue waves) is also considered, where random Gaussian generation of sea surface roughness is accompanied by the parametric excitation.

Fulltext pdf (1.6 MB)
Fulltext is also available at DOI: 10.3367/UFNe.0186.201601e.0075
Keywords: stochastic equations, intermittency, Lyapunov characteristic parameter, typical realization curve, dynamical localization, statistical topography, clustering
PACS: 05.40.−a, 05.45.−a, 46.65.+g, 47.27.−i (all)
DOI: 10.3367/UFNe.0186.201601e.0075
URL: https://ufn.ru/en/articles/2016/1/d/
000374119000003
2-s2.0-84962844410
2016PhyU...59...67K
Citation: Klyatskin V I "Stochastic structure formation in random media" Phys. Usp. 59 67–95 (2016)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 29th, June 2015, revised: 19th, November 2015, 24th, November 2015

Оригинал: Кляцкин В И «Стохастическое структурообразование в случайных средах» УФН 186 75–104 (2016); DOI: 10.3367/UFNr.0186.201601e.0075

References (70) ↓ Cited by (8) Similar articles (9)

  1. Shcherbakov R N Usp. Fiz. Nauk 184 153 (2014); Shcherbakov R N Phys. Usp. 57 143 (2014)
  2. Nicolis G, Prigogin I Exploring Complexity, An Introduction (New York: W.H. Freeman and Co., 1989); Per. na russk. yaz., Nikolis G, Prigozhin I Poznanie Slozhnogo. Vvedenie (M.: URSS, 2008)
  3. Klyatskin V I Prikl. Matem. Mekh. 33 889 (1969); Klyatskin V I J. Appl. Math. Mech. 33 864 (1969)
  4. Klyatskin V I Izv. RAN. Fiz. Atm. Okeana 31 749 (1995); Klyatskin V I Izv. Atmos. Ocean. Phys. 31 717 (1995); Klyatskin V, Gurarie D Physica D 98 466 (1996)
  5. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986); Per. na angl. yaz., Landau L D, Lifshitz E M Fluid Mechanics 2nd ed. (Oxford: Pergamon Press, 1987)
  6. Hopf E, Titt E W J. Rational Mech. Anal. 2 587 (1953)
  7. Kraichnan R H, Montgomery D Rep. Prog. Phys. 43 547 (1980)
  8. Hopfinger E J, Browand F K Nature 295 393 (1982)
  9. Griffiths R W, Hopfinger E J Deep Sea Res. A 31 245 (1984)
  10. Boubnov B M, Golitsyn G S J. Fluid Mech. 167 503 (1986)
  11. Hopfinger E J Theoretical And Applied Mechanics (Eds P Germain, M Piau, D Caillerie) (Amsterdam: Elsevier, 1989) p. 117
  12. Boubnov B M, Golitsyn G S Convection In Rotating Fluids (Dordrecht: Kluver Acad. Publ., 1995)
  13. Golitsyn G S Statistika i Dinamika Prirodnykh Protsessov i Yavlenii: Metody, Instrumentarii, Rezul’taty (M.: KRASAND, 2013)
  14. Pavlov V, Buisine D, Goncharov V Nonlin. Proc. Geophys. 8 9 (2001)
  15. Karimova S S, Lavrova O Yu, Solov’ev D M Issledovanie Zemli Kosmosa (5) 15 (2011); Karimova S S, Lavrova O Yu, Solov’ev D M Atmos. Ocean. Phys. 49 1006 (2012)
  16. Karimova S Adv. Space Res. 50 1107 (2012)
  17. Klyatskin V I Lectures On Dynamics Of Stochastic Systems (Boston, MA: Elsevier, 2010)
  18. Klyatskin V I Ocherki Po Dinamike Stokhasticheskikh Sistem (M.: KRASAND, 2012)
  19. Klyatskin V I Statisticheskii Analiz Kogerentnykh Yavlenii v Stokhasticheskikh Dinamicheskikh Sistemakh (M: KRASAND, 2015)
  20. Klyatskin V I Stochastic Equations: Theory And Applications In Acoustics, Hydrodynamics, Magnetohydrodynamics, And Radiophysics Vol. 1, 2 (Helderberg: Springer, 2015)
  21. Klyatskin V I Usp. Fiz. Nauk 182 1235 (2012); Klyatskin V I Phys. Usp. 55 1152 (2012)
  22. Klyatskin V I Chaos And Complex Systems. Proc. Of The 4th Intern. Interdisciplinary Chaos Symp. (Eds S G Stavrinides et al.) (Heidelberg: Springer-Verlag, 2013) p. 69
  23. Klyatskin V I Teor. Mat. Fiz. 176 495 (2013); Klyatskin V I Teor. Math. Phys. 176 1252 (2013)
  24. Klyatskin V I Russ. J. Math. Phys. 20 295 (2013)
  25. Klyatskin V I Usp. Fiz. Nauk 181 457 (2011); Klyatskin V I Phys. Usp. 54 441 (2011)
  26. Zel’dovich Ya B i dr. Zh. Eksp. Teor. Fiz. 89 2061 (1985); Zel’dovich Ya B et al. Sov. Phys. JETP 62 1188 (1985)
  27. Zel’dovich Ya B i dr. Usp. Fiz. Nauk 152 3 (1987); Zel’dovich Ya B et al. Sov. Phys. Usp. 30 353 (1987)
  28. Klyatskin V I Dinamicheskie Sistemy 4 193 (2014)
  29. Batchelor G K, Townsend A A Proc. R. Soc. Lond. A 199 238 (1949)
  30. Batchelor G K, Howells I D, Townsend A A J. Fluid Mech. 5 113 (1959)
  31. Monin A C, Yaglom A M Statisticheskaya Gidrodinamika Vol. 2 (M.: Nauka, 1967); Per. na russk. yaz., Monin A S, Yaglom A M Statistical Fluid Mechanics Vol. 2 (Cambridge, Mass.: MIT Press, 1975)
  32. Zakharov V "Bezumnye volny" http://http://www.youtube.com/watch?v=Bt3ZOswGd-4; Zakharov V "Volny-ubiitsy" http://www.zoomby.ru/watch/114832-academia
  33. Ruzmaikin A A Usp. Fiz. Nauk 184 297 (2014); Ruzmaikin A A Phys. Usp. 57 289 (2014)
  34. Anderson P W Phys. Rev. 109 1492 (1958)
  35. Lifshits I M, Gredeskul S A, Pastur L A Vvedenie v Teoriyu Neuporyadochennykh Sistem (M.: Nauka, 1982); Per. na angl. yaz., Lifshits I M, Gredeskul S A, Pastur L A Introduction To The Theory Of Disordered Solids (New York: John Wiley, 1988)
  36. Klyatskin V I, Saichev A I Usp. Fiz. Nauk 162 (3) 161 (1992); Klyatskin V I, Saichev A I Phys. Usp. 35 231 (1992)
  37. Mikhailov A S, Uporov I V Usp. Fiz. Nauk 144 79 (1984); Mikhailov A S, Uporov I V Sov. Phys. Usp. 27 695 (1984)
  38. Klyatskin V I, Saichev A I Zh. Eksp. Teor. Fiz. 111 1297 (1997); Klyatskin V I, Saichev A I JETP 84 716 (1997)
  39. Klyatskin V I, Chkhetiani O G Zh. Eksp. Teor. Fiz. 136 400 (2009); Klyatskin V I, Chkhetiani O G JETP 109 345 (2009)
  40. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982); Per. na angl. yaz., Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  41. Klyatskin V I Usp. Fiz. Nauk 174 177 (2004); Klyatskin V I Phys. Usp. 47 169 (2004)
  42. Malyanov D gazeta.ru, 17.06.2011 (2011); Malyanov D http://www.gazeta.ru/science/2011/06/17_a_3664677.shtml; Atkinson N Universe Today, Space and Astronomy News, 10 June, 2011 (2011); Atkinson N http://www.universetoday.com/86446/voyagers-find-giant-jacuzzi-like-bubbles-at-edge-of-solar-system/
  43. Klyatskin V I Usp. Fiz. Nauk 178 419 (2008); Klyatskin V I Phys. Usp. 51 395 (2008)
  44. Klyatskin V I Usp. Fiz. Nauk 179 547 (2009); Klyatskin V I Phys. Usp. 52 514 (2009)
  45. Zavorotnyi V U, Klyatskin V I, Tatarskii V I Zh. Eksp. Teor. Fiz. 73 481 (1977); Zavorotnyi V U, Klyatskin V I, Tatarskii V I Sov. Phys. JETP 46 252 (1977)
  46. Klyatskin V I Ctokhasticheskie Uravneniya i Volny v Sluchaino-neodnorodnykh Sredakh (M.: Fizmatlit, 1980); Klyatskin V I Ondes Et Équations Stochastiques Dans Les Milieus Aléatoirement Non Homogènes (Besançon-Cedex: Les éditions de Physique, 1985)
  47. Klyatskin V I, Yakushkin I G Zh. Eksp. Teor. Fiz. 111 2044 (1997); Klyatskin V I, Yakushkin I G JETP 84 1114 (1997)
  48. Klyatskin V I, El’perin T Zh. Eksp. Teor. Fiz. 122 327 (2002); Klyatskin V I, Elperin T JETP 95 328 (2002)
  49. Maxey M R J. Fluid Mech. 174 441 (1987)
  50. Klyatskin V I Zh. Eksp. Teor. Fiz. 126 1153 (2004); Klyatskin V I JETP 99 1005 (2004)
  51. Izrael’ Yu A Radioaktivnoe Zagryaznenie Prirodnykh Sred v Rezul’tate Avarii na Chernobyl’skoi Atomnoi Stantsii (k 20-letiyu Avarii) (M.: Komtekhprint, 2006); Izrael’ Yu A http://www.ibrae.ac.ru/images/stories/ibrae/chernobyl/israel.pdf
  52. Gurbatov S N, Saichev A I, Shandarin S F Usp. Fiz. Nauk 182 233 (2012); Gurbatov S N, Saichev A I, Shandarin S F Phys. Usp. 55 223 (2012)
  53. Rytov S M, Kravtsov Yu A, Tatarskii V I Vvedenie v Statisticheskuyu Radiofiziku Vol. 1, 2 (M.: Nauka, 1977, 1978); Per. na angl. yaz., Rytov S M, Kravtsov Yu A, Tatarskii V I Principles Of Statistical Radiophysics Vol. 1 - 4 (1987 - 1989)
  54. Klyatskin V I Teor. Mat. Fiz. 172 415 (2012); Klyatskin V I Teor. Math. Phys. 172 1243 (2012)
  55. Klyatskin V I, Yakushkin I G Zh. Eksp. Teor. Fiz. 118 849 (2000); Klyatskin V I, Yakushkin I G JETP 91 736 (2000)
  56. Klyatskin V I, Koshel’ K V Usp. Fiz. Nauk 170 771 (2000); Klyatskin V I, Koshel’ K V Phys. Usp. 43 717 (2000)
  57. Klyatskin V I Usp. Fiz. Nauk 181 457 (2011); Klyatskin V I Phys. Usp. 54 441 (2011)
  58. Klyatskin V I, Koshel K V Phys. Rev. E 91 063003 (2015)
  59. Kurkin A A, Pelinovskii E N Volny-ubiitsy: Fakty, Teoriya i Modelirovanie (N. Novgorod: NGTU, 2004)
  60. Kharif C, Pelinovsky E, Slunyaev A Rogue Waves In The Ocean (Berlin: Springer, 2009)
  61. Dysthe K, Krogstad H E, Muller P Annu. Rev. Fluid Mech. 40 287 (2008)
  62. Christou M, Ewans K J. Phys. Oceanogr. 44 2317 (2014)
  63. Ruban V P Pis’ma ZhETF 94 194 (2011); Ruban V P JETP Lett. 94 177 (2011)
  64. Ruban V P Pis’ma ZhETF 95 550 (2012); Ruban V P JETP Lett. 95 486 (2012)
  65. Ruban V P Pis’ma ZhETF 97 215 (2013); Ruban V P JETP Lett. 97 188 (2013)
  66. Ruban V P Pis’ma ZhETF 97 788 (2013); Ruban V P JETP Lett. 97 686 (2013)
  67. Klyatskin V I Teor. Mat. Fiz. 180 127 (2014); Klyatskin V I Theor. Math. Phys. 180 850 (2014)
  68. http://en.wikipedia.org/wiki/File:Ile_de_ré.JPG
  69. Metzger J J, Fleischmann R, Geisel T Phys. Rev. Lett. 112 203903 (2014)
  70. Klyatskin V I, Koshel’ K V Teor. Mat. Fiz. 186 (3) (2016), v pechati; Klyatskin V I, Koshel’ Theor. Math. Phys. 186 (3) (2016), in press
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions