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Reviews of topical problems


Intermittency in random media

 a, , ,
a All-Russian Scientific Research Institute of Experimental Physics — Federal Nuclear Centre, prosp. Mira 37, Sarov, Nizhny Novgorod region, 607190, Russian Federation

Some specific structures in which a growing quantity reaches record high values typically arise for instabilities in random media. Despite the rarity of these concentrations, they dominate the integral characteristics of the growing quantity (the mean value, the mean square value, etc.). The appearance of such structures is called ``intermittency''. The geometric properties of intermittent structures depend strongly on whether the growing quantity is a scalar or a vector. The scalar case is illustrated here by the example of an instability which arises in problems of chemical kinetics. The vector case is illustrated by the problem of the selfexcitation of a magnetic field in a random flow of a conducting fluid.

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Fulltext is also available at DOI: 10.1070/PU1987v030n05ABEH002867
PACS: 05.40.−a, 47.32.C− (all)
DOI: 10.1070/PU1987v030n05ABEH002867
URL: https://ufn.ru/en/articles/1987/5/a/
Citation: Zel’dovich Ya B, Molchanov S A, Ruzmaikin A A, Sokolov D D "Intermittency in random media" Sov. Phys. Usp. 30 353–369 (1987)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Çåëüäîâè÷ ß Á, Ìîë÷àíîâ Ñ À, Ðóçìàéêèí À À, Ñîêîëîâ Ä Ä «Ïåðåìåæàåìîñòü â ñëó÷àéíîé ñðåäå» ÓÔÍ 152 3–32 (1987); DOI: 10.3367/UFNr.0152.198705a.0003

References (57) Cited by (194) ↓ Similar articles (20)

  1. Satz H Mehr als die Summe der Teile Chapter 13 (2024) p. 157
  2. Gopalakrishnan K, Singh N K ApJ 970 64 (2024)
  3. Grachev D  A, Elistratov S  A, Mikhailov E  A Bull. Lebedev Phys. Inst. 51 140 (2024)
  4. Sirota V A, Il’yn A S et al 36 (2) (2024)
  5. Kutsenko V, Molchanov S, Yarovaya E Mathematics 12 550 (2024)
  6. Yakushkin I G Izv. Atmos. Ocean. Phys. 59 150 (2023)
  7. Mammadova A E, Sokoloff D D Moscow Univ. Phys. 78 591 (2023)
  8. Flandoli F, Luongo E Lecture Notes In Mathematics Vol. Stochastic Partial Differential Equations in Fluid MechanicsTransport Noise in the Heat Equation2330 Chapter 3 (2023) p. 75
  9. Dorogovtsev A A, Weiss A Stoch. Dyn. 23 (07) (2023)
  10. Kutsenko V A, Sokoloff D D, Yarovaya E B J. Exp. Theor. Phys. 136 498 (2023)
  11. Mammadova A E, Sokoloff D D VMU (¹5_2023) 2350102–1 (2023)
  12. Berger Q, Chong C, Lacoin H Commun. Math. Phys. 402 2215 (2023)
  13. Buts V A, Zagorodny A G 3 (2023)
  14. Buts V A, Kuzmin V V 16 (2023)
  15. Kutsenko V, Yarovaya E Stochastic Models 39 60 (2023)
  16. GRAHOVAC DANIJEL, LEONENKO NIKOLAI N, TAQQU MURAD S Fractals 30 (07) (2022)
  17. Gonzalez I, Horton E, Kyprianou A E Probab. Theory Relat. Fields 184 805 (2022)
  18. Levashov N N, Popov V Yu et al Cosmic Res 60 9 (2022)
  19. Grahovac D Statistics & Probability Letters 187 109507 (2022)
  20. Flandoli F, Pappalettera U Stoch PDE: Anal Comp 10 964 (2022)
  21. Smerlak M EPL 134 28002 (2021)
  22. Sokoloff D D, Chikina A A, Illarionov E A Astron. Rep. 65 362 (2021)
  23. Gómez G I T, Zanette D H J. Phys. Complex. 2 035020 (2021)
  24. Vatutin V A, Dyakonova E E Russ. Math. Surv. 76 1019 (2021)
  25. Mizerski K A J. Fluid Mech. 926 (2021)
  26. Smerlak M Journal Of Theoretical Biology 522 110699 (2021)
  27. Bauer M, Krapivsky P L, Mallick K Phys. Rev. E 103 (2) (2021)
  28. Vatutin V A, Dyakonova E E Uspekhi Matematicheskikh Nauk 76 71 (2021)
  29. Perkowski N, Rosati T Ann. Probab. 49 (2) (2021)
  30. Lyakhov G A, Shcherbakov I A, Shermeneva M A Phys. Wave Phen. 28 236 (2020)
  31. Grahovac D, Leonenko N N, Taqqu M S J Theor Probab 33 1801 (2020)
  32. Yushkov E V, Lukin A S, Sokoloff D D J. Exp. Theor. Phys. 130 935 (2020)
  33. Bogomolov S V, Esikova N B Math Models Comput Simul 12 257 (2020)
  34. Kuchar A, Sacha P et al Weather Clim. Dynam. 1 481 (2020)
  35. Meng X, Nane E Fract Calc Appl Anal 23 224 (2020)
  36. Zanette D H, Manrubia S 30 (3) (2020)
  37. Grahovac D, Leonenko N N, Taqqu M S Stochastic Processes And Their Applications 129 5113 (2019)
  38. Bogomolov S V, Bogomolov S V i dr Matematicheskoe Modelirovanie 31 120 (2019)
  39. Grahovac D, Leonenko N N et al Bernoulli 25 (3) (2019)
  40. Galich N E Lecture Notes In Networks And Systems Vol. Proceedings of SAI Intelligent Systems Conference (IntelliSys) 2016Self-regulation and Covariance of Intermittent DNA Activity in the Major Networks Inside Cells15 Chapter 77 (2018) p. 1113
  41. Mikhailov E A, Pushkarev V V Astrophys. Bull. 73 425 (2018)
  42. Ivanitskii G R Phys.-Usp. 61 871 (2018)
  43. Grahovac D, Leonenko N N, Taqqu M S Statistics & Probability Letters 137 235 (2018)
  44. Rybakov D, Lamazhapov Kh et al MATEC Web Conf. 209 00024 (2018)
  45. Mikhailov E A, Grachev D A ComBAO 346 (2018)
  46. Titov V V, Stepanov R A, Sokoloff D D J. Exp. Theor. Phys. 126 566 (2018)
  47. Kalinin A O, Sokoloff D D, Tutubalin V N Moscow Univ. Phys. 72 449 (2017)
  48. Bogomolov S V, Esikova N B, Kuvshinnikov A E Math Models Comput Simul 8 533 (2016)
  49. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 7 (2016) p. 123
  50. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 1 (2016) p. 1
  51. Klyatskin V I Uspekhi Fizicheskikh Nauk 186 75 (2016)
  52. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 2 (2016) p. 19
  53. Makarenko A V Tech. Phys. 61 265 (2016)
  54. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 8 (2016) p. 159
  55. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 5 (2016) p. 85
  56. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 6 (2016) p. 99
  57. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 3 (2016) p. 43
  58. König W The Parabolic Anderson Model Pathways In Mathematics Chapter 4 (2016) p. 71
  59. Grahovac D, Leonenko N N et al J Stat Phys 165 390 (2016)
  60. Bakunin O G Uspekhi Fizicheskikh Nauk 185 271 (2015) [Bakunin O G Phys.-Usp. 58 252 (2015)]
  61. Zelenyi L M, Bykov A M et al J. Plasma Phys. 81 (4) (2015)
  62. Makarenko A V J. Exp. Theor. Phys. 120 912 (2015)
  63. Belovolova L V, Glushkov M V, Timashev S F Phys. Wave Phen. 23 105 (2015)
  64. Sokoloff D, Illarionov E A J. Plasma Phys. 81 (4) (2015)
  65. Shukurov A, Sokoloff D, Schekochihin A J. Plasma Phys. 81 (4) (2015)
  66. Galich N E Biophys. Rev. Lett. 10 187 (2015)
  67. Sokolov D D, Stepanov R A, Frick P G Uspekhi Fizicheskikh Nauk 184 313 (2014) [Sokoloff D D, Stepanov R A, Frick P G Phys.-Usp. 57 292 (2014)]
  68. Sokolov D D, Stepanov R A, Frick P G Uspekhi Fizicheskikh Nauk 184 313 (2014) [Popov V S Phys.-Usp. 57 413 (2014)]
  69. Solomon S, Golo N SSRN Journal (2014)
  70. Sidorova N, Twarowski A Ann. Probab. 42 (4) (2014)
  71. Klyatskin V I, Klyatskin V I Teoreticheskaya Matematicheskaya Fizika 180 112 (2014) [Klyatskin V I Theor Math Phys 180 850 (2014)]
  72. Borodin A, Petrov L Probab. Surveys 11 (none) (2014)
  73. Popov V S Uspekhi Fizicheskikh Nauk 184 451 (2014)
  74. Piterbarg V I Wiley StatsRef: Statistics Reference Online 1 (2014)
  75. Snopok B A Theor Exp Chem 50 67 (2014)
  76. Klyatskin V I, Klyatskin V I Teoreticheskaya Matematicheskaya Fizika 176 494 (2013) [Klyatskin V I Theor Math Phys 176 1252 (2013)]
  77. Bakunin O G Uspekhi Fizicheskikh Nauk 183 1237 (2013) [Bakunin O G Phys.-Usp. 56 1132 (2013)]
  78. Klyatskin V I Russ. J. Math. Phys. 20 295 (2013)
  79. Galich N E OJBIPHY 03 232 (2013)
  80. Pavlos G P, Karakatsanis L P, Xenakis M N Physica A: Statistical Mechanics And Its Applications 391 6287 (2012)
  81. Ivanitskii G R Uspekhi Fizicheskikh Nauk 182 1238 (2012)
  82. Piterbarg V I Encyclopedia of Environmetrics 1 (2012)
  83. Bykov A M, Ellison D C, Renaud M Space Sci Rev 166 71 (2012)
  84. Makarenko A V Tech. Phys. Lett. 38 804 (2012)
  85. Abramenko V I Proc. IAU 8 289 (2012)
  86. Klyatskin V I, Klyatskin V I Teor. Mat. Fiz. 172 415 (2012)
  87. Krapivsky P L, Mallick K J. Stat. Mech. 2011 P01015 (2011)
  88. Chichigina O A, Dubkov A A et al Phys. Rev. E 84 (2) (2011)
  89. Bykov A M, Ellison D C, Renaud M Space Sciences Series Of ISSI Vol. Large-Scale Magnetic Fields in the UniverseMagnetic Fields in Cosmic Particle Acceleration Sources39 Chapter 3 (2011) p. 71
  90. Wolff A, Lohmar I et al J. Stat. Mech. 2011 P10029 (2011)
  91. Grachev D A J Math Sci 174 555 (2011)
  92. Makhnovskii Yu A, Berezhkovskii A M et al J. Phys. Chem. B 115 3992 (2011)
  93. Klyatskin V I Uspekhi Fizicheskikh Nauk 181 457 (2011)
  94. Grachev D A Math Notes 87 336 (2010)
  95. Knyazeva I S, Makarenko N G, Karimova L M Astron. Rep. 54 747 (2010)
  96. Grachev D A Moscow Univ. Math. Bull. 65 213 (2010)
  97. König W, Lacoin H et al Ann. Probab. 37 (1) (2009)
  98. Grachev D A J Math Sci 160 128 (2009)
  99. Dalang R C, Mueller C Ann. Inst. H. Poincaré Probab. Statist. 45 (4) (2009)
  100. van der Hofstad R, Mörters P, Sidorova N Ann. Appl. Probab. 18 (6) (2008)
  101. Gang Ch, Di-Kai L, Lian-Shou L Eur. Phys. J. A 37 227 (2008)
  102. Bakunin O G Reviews Of Plasma Physics Vol. Reviews of Plasma PhysicsCorrelations and Anomalous Transport Models24 Chapter 2 (2008) p. 53
  103. Lamazhapov Kh D, Alchagirov B B, Yakovlev V M Tech. Phys. Lett. 32 489 (2006)
  104. Ma Y G Eur. Phys. J. A 30 227 (2006)
  105. Ma Y G Dynamics and Thermodynamics with Nuclear Degrees of Freedom Chapter 18 (2006) p. 227
  106. Wilkinson D M Eur. Phys. J. B 43 221 (2005)
  107. CHICHIGINA O, VALENTI D, SPAGNOLO B Fluct. Noise Lett. 05 L243 (2005)
  108. Jones B J T, Martínez V J et al Rev. Mod. Phys. 76 1211 (2005)
  109. Gärtner J, König W Interacting Stochastic Systems Chapter 8 (2005) p. 153
  110. Artyushkova M E, Sokolov D D Astron. Rep. 49 520 (2005)
  111. Sreenivasan K R, Bershadskii A, Niemela J J Phys. Rev. E 71 (3) (2005)
  112. Dedikov S Yu, Shchekinov Yu A Astron. Rep. 48 9 (2004)
  113. Alkhimov V I, Alkhimov V I Teor. Mat. Fiz. 139 512 (2004)
  114. Bershadskii A, Sreenivasan K R Phys. Rev. Lett. 93 (6) (2004)
  115. Abramenko V I Astron. Rep. 47 151 (2003)
  116. Bakunin O G Uspekhi Fizicheskikh Nauk 173 757 (2003)
  117. Bakunin O G Plasma Phys. Rep. 29 955 (2003)
  118. Coles P The Early Universe and the Cosmic Microwave Background: Theory and Observations Chapter 12 (2003) p. 219
  119. Abramenko V I Astron. Rep. 46 161 (2002)
  120. Gang Ch, Lian-Shou L Chinese Phys. Lett. 19 1271 (2002)
  121. Coles P 330 421 (2002)
  122. Matarrese S, Mohayaee R 329 37 (2002)
  123. Aksel’rod E G, Kuz’min A N et al Tech. Phys. Lett. 27 529 (2001)
  124. Lamburt V G, Sokolov D D, Tutubalin V N Astron. Rep. 44 659 (2000)
  125. Gribova E Z, Zhukova I S et al Radiophys Quantum Electron 43 411 (2000)
  126. Zhukova I S, Saichev A I Journal Of Applied Mathematics And Mechanics 64 601 (2000)
  127. Jones B J T Monthly Notices Of The Royal Astronomical Society 307 376 (1999)
  128. Tsinober A Lecture Notes In Physics Vol. Chaos, Kinetics and Nonlinear Dynamics in Fluids and PlasmasTurbulence: Beyond phenomenology511 Chapter 5 (1998) p. 83
  129. Saichev A I, Zhukova I S Lecture Notes In Physics Vol. Chaos, Kinetics and Nonlinear Dynamics in Fluids and PlasmasThe arising and evolution of the passive tracer clusters in compressible random media511 Chapter 16 (1998) p. 353
  130. Barate R, Buskulic D et al Physics Reports 294 1 (1998)
  131. Manrubia S C, Zanette D H Phys. Rev. E 58 295 (1998)
  132. Zanette D H, Manrubia S C Phys. Rev. Lett. 79 523 (1997)
  133. Zhukova I S, Saichev A I Journal Of Applied Mathematics And Mechanics 61 765 (1997)
  134. Kondratyev V N, Lutz H O, Ayik S 106 7766 (1997)
  135. Meyer-Ortmanns H Rev. Mod. Phys. 68 473 (1996)
  136. Comprehensive Chemical Kinetics Vol. Modern Aspects of Diffusion-Controlled Reactions - Cooperative Phenomena in Bimolecular ProcessesChapter 2 Basic methods for describing chemical kinetics in condensed media: Continuum models34 (1996) p. 53
  137. Miller J, Wang Ja Phys. Rev. Lett. 76 1461 (1996)
  138. Mikhailov A S, Loskutov A Yu Springer Series In Synergetics Vol. Foundations of Synergetics IIBirth-Death Systems52 Chapter 10 (1996) p. 184
  139. Cherry M L, Da̧browska A et al Phys. Rev. C 53 1532 (1996)
  140. De Wolf E A, Dremin I M, Kittel W Physics Reports 270 1 (1996)
  141. Belkacem M, Latora V, Bonasera A Phys. Rev. C 52 271 (1995)
  142. Kubo T, Belkacem M et al Z. Physik A - Hadrons And Nuclei 352 145 (1995)
  143. Bożek P, Płoszajczak M, Botet R Physics Reports 252 101 (1995)
  144. Mikhailov A S, Zanette D H Chaos, Solitons & Fractals 6 367 (1995)
  145. Bächler J, Bartke J et al Z. Phys. C - Particles And Fields 61 551 (1994)
  146. Abdullaev S S 4 569 (1994)
  147. Zanette D, Mikhailov A Phys. Rev. E 50 1638 (1994)
  148. Bezák V Physica A: Statistical Mechanics And Its Applications 206 127 (1994)
  149. Kleeorin N, Rogachevskii I Phys. Rev. E 50 2716 (1994)
  150. Zanette D H Phys. Rev. E 49 2779 (1994)
  151. Sokolova E V Math Notes 55 430 (1994)
  152. Latora V, Belkacem M, Bonasera A Phys. Rev. Lett. 73 1765 (1994)
  153. Tomilin M G, Ivanyuk G Yu Liquid Crystals 14 1599 (1993)
  154. Schmidt H R, Schukraft J J. Phys. G: Nucl. Part. Phys. 19 1705 (1993)
  155. Ruzmaikin A, Liewer P C, Feynman J Geophysical & Astrophysical Fluid Dynamics 73 163 (1993)
  156. Sarkisyan E K, Gelovani L K et al Physics Letters B 318 568 (1993)
  157. Ghosh D, Deb A et al Europhys. Lett. 23 91 (1993)
  158. Elattari B, Richert J, Wagner P Phys. Rev. Lett. 69 45 (1992)
  159. Hakioḡlu T Phys. Rev. D 45 3079 (1992)
  160. DeAngelis A R, Gross D H E, Heck R Nuclear Physics A 537 606 (1992)
  161. Rabinovich M I, Fabrikant A L, Tsimring L Sh Uspekhi Fizicheskikh Nauk 162 1 (1992)
  162. Jaqaman H R, DeAngelis A R et al Nuclear Physics A 541 492 (1992)
  163. Bożek P, Płoszajczak M, Tucholski A Nuclear Physics A 539 693 (1992)
  164. Gross D H E, Ecker A, Deangelis A R Annalen Der Physik 504 340 (1992)
  165. Englman R J Stat Phys 66 1383 (1992)
  166. Elattari B, Richert J, Wagner P Nuclear Physics A 538 403 (1992)
  167. Ruzmaikin A, Shukurov A, Sokoloff D J. Geophys. Res. 97 15007 (1992)
  168. Pan J Phys. Rev. D 46 R19 (1992)
  169. Mikhailov A Physica A: Statistical Mechanics And Its Applications 188 367 (1992)
  170. Gross D H E, DeAngelis A R et al Phys. Rev. Lett. 68 146 (1992)
  171. Mikhailov A S J. Phys. A: Math. Gen. 24 L757 (1991)
  172. Kirsch W, Pastur L A International Series Of Numerical Mathematics / Internationale Schriftenreihe Zur Numerischen Mathematik / Série Internationale D’Analyse Numérique Vol. Random Partial Differential EquationsLarge Time Behaviour of Moments of Fundamental Solutions of the Random Parabolic Equation102 Chapter 9 (1991) p. 127
  173. Bogachev L V, Molchanov S A Theor Math Phys 87 512 (1991)
  174. Molchanov S A Acta Applicandae Mathematicae 22 139 (1991)
  175. Ploszajczak M, Tucholski A Nuclear Physics A 523 651 (1991)
  176. Mikhailov A S, Loskutov A Yu Springer Series In Synergetics Vol. Foundations of Synergetics IIPopulation Explosions52 Chapter 10 (1991) p. 138
  177. Derado I, Jancso G et al Z. Phys. C - Particles And Fields 47 23 (1990)
  178. Ochs W Phys. Bl. 46 123 (1990)
  179. Ploszajczak M, Tucholski A Phys. Rev. Lett. 65 1539 (1990)
  180. Gärtner J, Molchanov S A Commun.Math. Phys. 132 613 (1990)
  181. Hwa R C Nuclear Physics B - Proceedings Supplements 12 307 (1990)
  182. Bożek P, Płoszajczak M Physics Letters B 251 623 (1990)
  183. Bogachev L V, Molchanov S A Theor Math Phys 81 1207 (1989)
  184. Laskin N V J. Phys. A: Math. Gen. 22 1565 (1989)
  185. RUZMAIKIN A A, SOKOLOFF D D Turbulence and Nonlinear Dynamics in MHD Flows (1989) p. 29
  186. Young G R, Albrecht R et al Nuclear Physics A 498 53 (1989)
  187. Mikhailov A S Physics Reports 184 307 (1989)
  188. Leschke H, Wonneberger S J. Phys. A: Math. Gen. 22 L1009 (1989)
  189. Satz H Nuclear Physics B 326 613 (1989)
  190. Shandarin S F, Zeldovich Ya B Rev. Mod. Phys. 61 185 (1989)
  191. Hwa R C Nuclear Physics B 328 59 (1989)
  192. Turko L Physics Letters B 227 149 (1989)
  193. Wosiek J Nuclear Physics B - Proceedings Supplements 9 640 (1989)
  194. Bialas A, Peschanski R Nuclear Physics B 308 857 (1988)
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