RSS feeds
РусскийEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1986

 / 

October

←  →

Reviews of topical problems


Dimensionalities and other geometric critical exponents in percolation theory


A review is given of the studies of the dimensionality characteristics of percolation clusters. The purely geometric nature of a percolation phase transition and the great variety of the quantities exhibiting critical behavior make this geometric approach both informative and useful. In addition to the fractal dimensionality of a cluster and its subsets (such as the backbone, hull, and other dimensionalities), it is necessary to introduce additional characteristics. For example, the maximum velocity of propagation of excitations is determined by the chemical dimensionality of a cluster, and the critical behavior of the conductivity, diffusion coefficient, etc., is determined by spectral (or other related to it) dimensionalities. Scaling relationships between different dimensionalities, as well as relationships between dimensionalities and conventional critical exponents are discussed.

Fulltext pdf (959 KB)
Fulltext is also available at DOI: 10.1070/PU1986v029n10ABEH003526
PACS: 64.60.Ak, 64.60.Fr (all)
DOI: 10.1070/PU1986v029n10ABEH003526
URL: https://ufn.ru/en/articles/1986/10/b/
Citation: Sokolov I M "Dimensionalities and other geometric critical exponents in percolation theory" Sov. Phys. Usp. 29 924–945 (1986)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Соколов И М «Размерности и другие геометрические критические показатели в теории протекания» УФН 150 221–255 (1986); DOI: 10.3367/UFNr.0150.198610b.0221

Cited by (141) ↓ Similar articles (20)

  1. Onishenko A O, Suslov E A et al Eurasian J. Phys. Funct. Mater. 8 14 (2024)
  2. Nechaev V N, Shuba A V, Gotsev D V Ferroelectrics 612 17 (2023)
  3. Cruz M-Á M, Ortiz Ju P et al Fractal Fract 7 231 (2023)
  4. Aryanfar A, Khoury M N et al Construction And Building Materials 379 131109 (2023)
  5. Kovylin R S, Yudin V V et al Materials 16 3177 (2023)
  6. Bondar M V Ukr. J. Phys. 56 988 (2022)
  7. Dolbin I V, Magomedov M A, Kozlov G V Russ Phys J 65 728 (2022)
  8. Kfir-Cohen Ya, Vaknin B P D, Havlin Sh EPL 137 41003 (2022)
  9. Domashevskaya E P, Mahdy M A et al Materials Chemistry And Physics 277 125480 (2022)
  10. Kozlitin R A, Udodov V N J. Phys.: Conf. Ser. 2094 022036 (2021)
  11. Paramonov A, Bushelenkov S Inf. Tehnol. Telekommun. 9 37 (2021)
  12. Zalutskii A A Crystallogr. Rep. 65 371 (2020)
  13. Rendevski S J, Dyussenbekov A M, Nurlanov F N Eur. J. Phys. 41 055802 (2020)
  14. Huang Ch-Yu, Lai Y-Ch, Liao Y-Ch ACS Appl. Electron. Mater. 1 718 (2019)
  15. Kozlov G V, Dolbin I V Phys. Solid State 61 39 (2019)
  16. Dong G, Fan J et al Proc. Natl. Acad. Sci. U.S.A. 115 6911 (2018)
  17. Herega A The Selected Models of the Mesostructure of Composites SpringerBriefs In Physics Chapter 1 (2018) p. 1
  18. Kryvchenko Yu TST (4 (14)) 153 (2018)
  19. Herega A The Selected Models of the Mesostructure of Composites SpringerBriefs In Physics Chapter 3 (2018) p. 17
  20. Kozlov G V, Dolbin I V J Appl Mech Tech Phy 59 765 (2018)
  21. Herega A The Selected Models of the Mesostructure of Composites SpringerBriefs In Physics Chapter 4 (2018) p. 27
  22. Herega A, Sukhanov V et al (AIP Conference Proceedings) Vol. 2051 (2018) p. 020105
  23. Herega A The Selected Models of the Mesostructure of Composites SpringerBriefs In Physics Chapter 2 (2018) p. 5
  24. Balankin A S, Mena B, Martínez C M A Physics Letters A 381 2665 (2017)
  25. Zadneprovski B I, Klyuev I Yu, Turkov V E Tech. Phys. Lett. 42 872 (2016)
  26. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 3 (2016) p. 59
  27. Katunin A, Krukiewicz K et al 16 32 (2016)
  28. Prostnev A S, Shub B R Russ. J. Phys. Chem. B 10 1022 (2016)
  29. Snarskii A A, Bezsudnov I V et al Transport Processes in Macroscopically Disordered Media Chapter 4 (2016) p. 41
  30. Zalutski A A Prot Met Phys Chem Surf 52 34 (2016)
  31. Kozlov G, Dolbin I et al Materials Behavior (2015) p. 149
  32. Kozlov G, Dolbin I et al Materials Behavior (2015) p. 161
  33. Herega A (AIP Conference Proceedings) Vol. 1683 (2015) p. 020071
  34. Zalutskii A A Tech. Phys. Lett. 40 909 (2014)
  35. Fractal Mechanics of Polymers (2014) p. 1
  36. Prostnev A S, Shub B R Russ. J. Phys. Chem. B 8 420 (2014)
  37. Fractal Mechanics of Polymers (2014) p. 37
  38. Muller G, Ringuedé A, Laberty-Robert Ch Langmuir 30 8889 (2014)
  39. Bakunin O G Uspekhi Fizicheskikh Nauk 183 257 (2013) [Bakunin O G Phys.-Usp. 56 243 (2013)]
  40. Rostami Kh R Phys. Solid State 55 1786 (2013)
  41. Kamilov I K, Daunov M I, Bashirov R R High Pressure Research 33 98 (2013)
  42. Stuchinsky V A Tech. Phys. Lett. 39 380 (2013)
  43. Prostnev A S, Shub B R Russ. J. Phys. Chem. B 7 568 (2013)
  44. Afanasyev D A, Ibrayev N Kh et al Journal Of Luminescence 136 358 (2013)
  45. Sokolov I M Mathematics of Complexity and Dynamical Systems Chapter 2 (2012) p. 13
  46. Antipov A A, Arakelyan S M et al Bull. Russ. Acad. Sci. Phys. 76 611 (2012)
  47. Bragin V A, Dushenok S A et al Russ. J. Phys. Chem. B 6 390 (2012)
  48. Herega A N, Drik N G, Ugol’nikov A P Uspekhi Fizicheskikh Nauk 182 555 (2012)
  49. Bondar N V, Brodyn M S Semiconductors 46 625 (2012)
  50. Vasin S I, Sherysheva E E, Filippov A N Colloid J 73 167 (2011)
  51. Vasin S I, Kharitonova T V, Filippov A N Colloid J 73 158 (2011)
  52. Dzhanakhmedov A Kh, Dyshin O A J. Frict. Wear 32 61 (2011)
  53. Bakunin O G Springer Series In Synergetics Vol. Chaotic FlowsTransport and Complex Structures10 Chapter 10 (2011) p. 165
  54. Bureeva M A, Volkova T V et al Russ Phys J 53 140 (2010)
  55. Sokolov I M Encyclopedia of Complexity and Systems Science Chapter 21 (2009) p. 309
  56. Yatsyshyn B P, Mikolaichuk A G et al Inorg Mater 45 386 (2009)
  57. Bakunin O G Reviews Of Plasma Physics Vol. Reviews of Plasma PhysicsCorrelations and Anomalous Transport Models24 Chapter 2 (2008) p. 53
  58. Bakunin O G Turbulence and Diffusion Springer Series In Synergetics Chapter 10 (2008) p. 147
  59. Klyucharev V V Glass Phys Chem 34 660 (2008)
  60. Baronskaya N A, Minyukova T P et al Chemical Engineering Journal 134 195 (2007)
  61. Pozdnyakov V A Bull. Russ. Acad. Sci. Phys. 71 1708 (2007)
  62. Pavlov A N, Anishchenko V S Uspekhi Fizicheskikh Nauk 177 859 (2007)
  63. Tsarev M V, Mokrushin V V Tech. Phys. 52 369 (2007)
  64. Dimov S V, Sipatrov A G et al Theor Found Chem Eng 41 184 (2007)
  65. Alekseev D V, Kazunina G A J Min Sci 42 43 (2006)
  66. Kozlov G, Lipatov Yu Chemical kinetics (2005) p. 484
  67. BAKUNIN O Chaos, Solitons & Fractals 23 1703 (2005)
  68. Novikov V U, Kozlov G V International Polymer Science And Technology 32 1 (2005)
  69. Burya O I, Kozlov H V, Chyhvintseva O P Mater Sci 41 349 (2005)
  70. Miichenko I P International Polymer Science And Technology 31 36 (2004)
  71. Kozlov G V, Dolbin I V, Zaikov G E J Of Applied Polymer Sci 94 1353 (2004)
  72. Bakunin O G Rep. Prog. Phys. 67 965 (2004)
  73. Kozlov G V, Zaikov G E J Of Applied Polymer Sci 92 3601 (2004)
  74. Bakunin O G Uspekhi Fizicheskikh Nauk 173 757 (2003)
  75. Bakunin O G Plasma Phys. Rep. 29 955 (2003)
  76. Bagnich S A, Konash A V J. Phys. A: Math. Gen. 36 1 (2003)
  77. Bakunin O G Plasma Phys. Control. Fusion 45 1909 (2003)
  78. Oleschko K, Korvin G et al Phys. Rev. E 67 (4) (2003)
  79. Iudin D I, Trakhtengerts V Y, Hayakawa M Phys. Rev. E 68 (1) (2003)
  80. Konash A, Bagnich S Lecture Notes In Computational Science And Engineering Vol. Interface and Transport DynamicsComputer Investigation of the Influence of the Internal Structure Topology on the Percolation Process in Two- and Three-Dimensional Inhomogeneous Systems32 Chapter 5 (2003) p. 65
  81. Geick R Landolt-Börnstein - Group III Condensed Matter Vol. Halide Perovskite-Type Layer Structures9.12.4.4 References for 9.12.427J3 Chapter 27 (2001) p. 485
  82. Geick R Landolt-Börnstein - Group III Condensed Matter Vol. Halide Perovskite-Type Layer Structures9.12.4.1 Static critical behaviour27J3 Chapter 20 (2001) p. 349
  83. Kozlov G V, Novikov V U Uspekhi Fizicheskikh Nauk 171 717 (2001)
  84. Sheintuch M Catalysis Reviews 43 233 (2001)
  85. Bagnich S A, Konash A V Phys. Solid State 43 2313 (2001)
  86. Novikov V U, Kozlov G V Russ. Chem. Rev. 69 347 (2000)
  87. Roldughin V I, Vysotskii V V Progress In Organic Coatings 39 81 (2000)
  88. Borman V D, Grekhov A M, Troyan V I J. Exp. Theor. Phys. 91 170 (2000)
  89. Kozlov G V, Afaunov V V, Lipatov Yu S J Eng Phys Thermophys 73 436 (2000)
  90. Bagnich S A Phys. Solid State 42 1775 (2000)
  91. Demidov B A, Efremov V P et al Tech. Phys. 45 870 (2000)
  92. Novikov V U, Kozlov G V Russ. Chem. Rev. 69 523 (2000)
  93. Vysotsky V V, Roldughin V I Colloids And Surfaces A: Physicochemical And Engineering Aspects 160 171 (1999)
  94. Demidov B A, Efremov V P et al Tech. Phys. 44 1413 (1999)
  95. Bagnich S A Chemical Physics 237 359 (1998)
  96. Kozlov G V, Novikov V U et al J Eng Phys Thermophys 71 241 (1998)
  97. Demidov B A, Efremov V P et al Tech. Phys. 43 1239 (1998)
  98. Sokolov I M, Mai J, Blumen A Journal Of Luminescence 76-77 377 (1998)
  99. Demidov B A, Efremov V P et al Tech. Phys. 42 1258 (1997)
  100. Demidov B A, Ivkin M V et al Tech. Phys. 42 1264 (1997)
  101. Cherepanov G P Solid Mechanics And Its Applications Vol. Methods of Fracture Mechanics: Solid Matter PhysicsFractals in Fracture of Solids51 Chapter 8 (1997) p. 275
  102. Sokolov I M, Mai J, Blumen A Phys. Rev. Lett. 79 857 (1997)
  103. Mazars M Phys. Rev. E 53 6297 (1996)
  104. Mishnaevsky L L Fatigue ’96 (1996) p. 1287
  105. Dzhabrailov V V, Meilanov R P J Eng Phys Thermophys 69 188 (1996)
  106. Irzhak V I, Kuzub L I Progress In Colloid & Polymer Science Vol. GelsKinetics of sorption processes in polymer gels102 Chapter 26 (1996) p. 138
  107. Davydov L N, Spolnik Z A Physica Status Solidi (b) 191 57 (1995)
  108. Cherepanov G P, Balankin A S, Ivanova V S Engineering Fracture Mechanics 51 997 (1995)
  109. Mishnaevskii L L J Eng Phys Thermophys 67 745 (1994)
  110. Nakayama T, Yakubo K, Orbach R L Rev. Mod. Phys. 66 381 (1994)
  111. Kadet V V, Musin R M, Selyakov V I Fluid Dyn 28 808 (1994)
  112. de Vries P, de Raedt H, Lagendijk A Computer Physics Communications 75 298 (1993)
  113. Branover H, Bershadskii A et al Boundary-Layer Meteorol 62 117 (1993)
  114. Melik-Gaikazov G V Combust Explos Shock Waves 29 1 (1993)
  115. Ozhovan M I, Dmitriev I E, Batyukhnova O G At Energy 74 241 (1993)
  116. Branover H, Bershadskii A et al Transport and Diffusion in Turbulent Fields Chapter 5 (1993) p. 117
  117. Lyakhimets S, Maziewski A et al 73 5942 (1993)
  118. Bershadskii A, Tsinober A Physics Letters A 165 37 (1992)
  119. Mal’shkov A V J Eng Phys Thermophys 62 297 (1992)
  120. Ozhovan M I, Kachalov M B J Eng Phys Thermophys 63 769 (1992)
  121. Isichenko M B Rev. Mod. Phys. 64 961 (1992)
  122. Bershadskii A G J Eng Phys Thermophys 62 182 (1992)
  123. Ragulya A V, Skorokhod V V Powder Metall Met Ceram 31 1006 (1992)
  124. Furgel’ I A, Molin O V et al J Eng Phys Thermophys 62 335 (1992)
  125. Dremin I M Surveys In High Energy Physics 6 141 (1992)
  126. Isichenko M B, Kalda J J Nonlinear Sci 1 255 (1991)
  127. Tretyakov A Yu, Burlatsky S F Solid State Communications 77 1 (1991)
  128. Khasanov M M, Abyzbaev I I Journal Of Engineering Physics 61 1516 (1991)
  129. Bershadskii A G Journal Of Engineering Physics 61 1188 (1991)
  130. Chukalkin Yu G, Shtirts V R, Goshchitskii B N Phys. Stat. Sol. (a) 125 301 (1991)
  131. Glushko S P, Kadet V V, Rostovskii N S J Appl Mech Tech Phys 32 138 (1991)
  132. Glushko S P, Kadet V V, Selyakov V I Fluid Dyn 24 727 (1990)
  133. Dremin I M Uspekhi Fizicheskikh Nauk 160 105 (1990)
  134. de Vries P, De Raedt H, Lagendijk A Phys. Rev. Lett. 62 2515 (1989)
  135. Vavriv D M, Ryabov V B USSR Computational Mathematics And Mathematical Physics 29 18 (1989)
  136. Akhromeyeva T S, Kurdyumov S P et al Physics Reports 176 189 (1989)
  137. Kadet V V, Selyakov V I Fluid Dyn 24 91 (1989)
  138. Nigmatullin R R, Sutugin N N Journal Of Engineering Physics 57 958 (1989)
  139. Beigel’zimer Ya E, Getmanskii A P Powder Metall Met Ceram 27 773 (1988)
  140. Pfeifer P Springer Series In Surface Sciences Vol. Chemistry and Physics of Solid Surfaces VIIFractals in Surface Science: Scattering and Thermodynamics of Adsorbed Films10 Chapter 10 (1988) p. 283
  141. Vitukhnovsky A G, Pyttel B L, Sokolov I M Physics Letters A 126 89 (1987)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions