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

Issues

 / 

1993

 / 

December

←  →

Reviews of topical problems


Application of fractals in condensed-matter physics

 a,
a Sumy State University, ul. Rimskogo-Korsakova 2, Sumy, 244007, Ukraine

Basic information about the theory of mono- and multifractal sets is presented. Geometric and thermodynamic descriptions are developed. The geometric picture is presented on the basis of the simplest examples of the Koch and Cantor fractal sets. An ultrametric space, representing the metric of a fractal set, is introduced on the basis of Cayley's hierarchical tree. The spectral characteristics of a multifractal formation are described. Attention is focused mainly on the application of the fractal concept for a thermodynamic system with partial memory loss, turbulent fluid flow, hierarchically coordinated set of statistical ensembles, Anderson's transition, and incommensurable and quasicrystalline structures.

Fulltext pdf (2 MB)
Fulltext is also available at DOI: 10.1070/PU1993v036n12ABEH002208
PACS: 64.60.Ak, 47.53.+n, 61.43.Hv, 61.44.−n (all)
DOI: 10.1070/PU1993v036n12ABEH002208
URL: https://ufn.ru/en/articles/1993/12/a/
Citation: Olemskoi A I, Flat A Ya "Application of fractals in condensed-matter physics" Phys. Usp. 36 (12) 1087–1128 (1993)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Олемской А И, Флат А Я «Использование концепции фрактала в физике конденсированной среды» УФН 163 (12) 1–50 (1993); DOI: 10.3367/UFNr.0163.199312a.0001

References (60) Cited by (112) ↓ Similar articles (20)

  1. Petrova E V, Tiunov E S et al Phys. Rev. Lett. 132 (5) (2024)
  2. Nikiforova N N, Oksengendler B L et al J. Surf. Investig. 18 1221 (2024)
  3. Arkashov N S, Seleznev V A Comput. Math. And Math. Phys. 64 441 (2024)
  4. Arkashov N S Sib. Adv. Math. 34 175 (2024)
  5. Mukherjee B, Srivardhan V et al Journal Of Asian Earth Sciences 271 106233 (2024)
  6. Çopuroğlu E, Mamedov B A Physica Status Solidi (b) 260 (6) (2023)
  7. Arkashov N S, Seleznev V A 33 (7) (2023)
  8. Rekhviashvili S Sh, Pskhu A V, Margushev Z Ch Tech. Phys. Lett. 48 39 (2022)
  9. Butenko P N, Hilarov V L, Obidov B A Phase Transitions 95 537 (2022)
  10. Arkashov N S Physica A: Statistical Mechanics And Its Applications 603 127795 (2022)
  11. Ryazanov V V Eur. Phys. J. B 94 (12) (2021)
  12. Kerefov M A, Kerefov B M J Math Sci 250 760 (2020)
  13. Pskhu A V, Rekhviashvili S Sh Moscow Univ. Phys. 75 316 (2020)
  14. Shevchuk T  M, Bordyuk M  A et al Metallofiz. Noveishie Tekhnol. 42 1293 (2020)
  15. Iashina E G, Altynbaev E V et al J. Synch. Investig. 14 429 (2020)
  16. Kushchenko O M, Rudyi S S et al Opt. Spectrosc. 128 1221 (2020)
  17. Butenko P N, Gilyarov V L et al Tech. Phys. 65 205 (2020)
  18. Rekhviashvili S Sh, Pskhu A V Tech. Phys. 64 1237 (2019)
  19. Makhmanov U, Kokhkharov A, Bakhramov S Fullerenes, Nanotubes And Carbon Nanostructures 27 273 (2019)
  20. Maldonado C, Salgado-García R J. Stat. Mech. 2019 033203 (2019)
  21. Iashina E G, Filatov M V et al J Appl Crystallogr 52 844 (2019)
  22. Gapontsev V L, Fedorov V A et al EURASIA J MATH SCI T 15 (3) (2019)
  23. Arkashov N S Comput. Math. And Math. Phys. 59 402 (2019)
  24. Smolanov N A J. Phys.: Conf. Ser. 1281 012078 (2019)
  25. Safiulina I A, Altynbaev E V et al Phys. Solid State 60 751 (2018)
  26. Nikiforova N N, Ashurov Kh B et al J. Synch. Investig. 12 154 (2018)
  27. Arkashov N S, Seleznev V A Theor Math Phys 193 1508 (2017)
  28. Iashina E G, Velichko E V et al Phys. Rev. E 96 (1) (2017)
  29. Rekhviashvili S Sh, Alikhanov A A Semiconductors 51 755 (2017)
  30. Lazarev S I, Golovin Yu M et al Pet. Chem. 56 423 (2016)
  31. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 5 (2016) p. 179
  32. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 4 (2016) p. 141
  33. Khatuntseva O N Numer. Analys. Appl. 8 81 (2015)
  34. Usov V V, Gopkalo E E et al Russ. Metall. 2015 759 (2015)
  35. Galiyarova N M Bull. Russ. Acad. Sci. Phys. 78 971 (2014)
  36. Kuzkova N, Yakunov A, Bilyi M Advances In Optical Technologies 2014 1 (2014)
  37. Marov M Ya, Kolesnichenko A V Astrophysics And Space Science Library Vol. Turbulence and Self-OrganizationStochastic-Thermodynamic Modeling of Developed Structured Turbulence389 Chapter 5 (2013) p. 295
  38. Gavrilova N D, Lotonov A M, Davydova A A Moscow Univ. Phys. 68 45 (2013)
  39. Kraynova G S, Frolov A M, Pisarenko T A AMR 718-720 85 (2013)
  40. Rostami Kh R Phys. Solid State 55 1786 (2013)
  41. Balankin A S, Mena B et al Phys. Rev. E 86 (5) (2012)
  42. Yudin V V, Yudin V V i dr Teoreticheskaya Matematicheskaya Fizika 173 71 (2012) [Yudin V V, Startzev E S Theor Math Phys 173 1387 (2012)]
  43. Maslovskaya A G, Barabash T K J. Synch. Investig. 6 37 (2012)
  44. Khamzin A A, Nigmatullin R R, Popov I I J. Phys.: Conf. Ser. 394 012013 (2012)
  45. Potirakis S M, Minadakis G, Eftaxias K Nat Hazards 64 641 (2012)
  46. Baskin E, Iomin A Computers & Mathematics With Applications 64 3302 (2012)
  47. Baskin E, Iomin A Chaos, Solitons & Fractals 44 335 (2011)
  48. Hierarchic Electrodynamics and Free Electron Lasers (2011) p. 211
  49. Khamzin A A, Nigmatullin R R et al J. Phys.: Conf. Ser. 324 012005 (2011)
  50. Rekhviashvili S Sh, Gavasheli D Sh Phys. Solid State 53 1822 (2011)
  51. Borukhov V T, Kvetko O M J. Comput. Syst. Sci. Int. 49 169 (2010)
  52. Khatuntseva O N Numer. Analys. Appl. 3 82 (2010)
  53. Sukhanov P P, Perukhin M Yu, Arkhireev V P International Polymer Science And Technology 37 23 (2010)
  54. Yudin V V, Yudin V V i dr Teor. Mat. Fiz. 164 88 (2010) [Yudin V V, Titov P L, Mikhalyuk A N Theor Math Phys 164 905 (2010)]
  55. Bazzaev A K, Shkhanukov-Lafishev M Kh Comput. Math. And Math. Phys. 50 1141 (2010)
  56. Sarkisov P D, Butusov O B et al Theor Found Chem Eng 44 838 (2010)
  57. Mihalyuk A N, Titov P L, Yudin V V Physica A: Statistical Mechanics And Its Applications 389 4127 (2010)
  58. Tropina N E, Petrovskaya Z N, Chernoglazova I O Semiconductors 43 1437 (2009)
  59. Artyomov V G, Kapralov P O et al Bull. Lebedev Phys. Inst. 36 209 (2009)
  60. Myslitskaya N A, Ivanov A M et al J Appl Spectrosc 76 777 (2009)
  61. Kolesnichenko A V Sol Syst Res 42 391 (2008)
  62. GARASCHENKO F G, KRUCHININ D S, NOVIKOV V E Int. J. Mod. Phys. B 22 3923 (2008)
  63. Samusev I G, Bryukhanov V V et al J Appl Spectrosc 74 230 (2007)
  64. Eftaxias K, Panin V E, Deryugin Y Y Tectonophysics 431 273 (2007)
  65. Borukhov V, Kvetko O 2007 International Workshop on Multidimensional (nD) Systems, (2007) p. 161
  66. Avdyukhina V M Phys. Solid State 47 397 (2005)
  67. Suleimanov B A, Abbasov E M, Efendieva A O J Eng Phys Thermophys 78 832 (2005)
  68. Olemskoi A I, Kharchenko D O, Knyaz’ I A Phys. Rev. E 71 (4) (2005)
  69. Karstina S G, Baktybekov K S, Vertyagina E N Russ Phys J 48 553 (2005)
  70. Usov V V, Shkatulyak N M Mater Sci 41 62 (2005)
  71. Kulkov S N, Mironov Yu P Tech. Phys. 49 505 (2004)
  72. Usov V V, Shkatulyak N M Russ Phys J 47 1139 (2004)
  73. Lisovskii F V, Lukashenko L I, Mansvetova E G Jetp Lett. 79 352 (2004)
  74. Stanislavskii A A, Stanislavskii A A Teor. Mat. Fiz. 138 491 (2004)
  75. Albuquerque E L, Cottam M G Polaritons in Periodic and Quasiperiodic Structures (2004) p. 125
  76. Avdyukhina V M, Anishchenko A A et al Phys. Solid State 46 411 (2004)
  77. Sotskov V A, Karpenko S V Tech. Phys. 48 100 (2003)
  78. Albuquerque E L, Cottam M G Physics Reports 376 225 (2003)
  79. Savenkov G G Tech. Phys. 47 1529 (2002)
  80. Meilanov R P, Yanpolov M S Tech. Phys. Lett. 28 30 (2002)
  81. Meilanov R P, Sveshnikova D A, Shabanov O M J. Phys. Chem. A 106 11771 (2002)
  82. Avdyukhina V M, Katsnelson A A et al Crystallogr. Rep. 47 362 (2002)
  83. Yudin V V, Karygina Yu A Crystallogr. Rep. 46 922 (2001)
  84. Manjavidze J, Sissakian A Physics Reports 346 1 (2001)
  85. Kuznetsov P V, Panin V E, Schreiber J Theoretical And Applied Fracture Mechanics 35 171 (2001)
  86. Afanas’eva R V, Maksimov A A, Ermakova T G Dokl. Phys. 46 829 (2001)
  87. Panin V, Kolubaev A et al Wear 249 860 (2001)
  88. Qiu W-Yu, Lü J Physics Letters A 272 353 (2000)
  89. Novikov V U, Kozlov G V Russ. Chem. Rev. 69 347 (2000)
  90. Galiyarova N Ferroelectrics 222 381 (1999)
  91. Arkhincheev V E J. Exp. Theor. Phys. 88 710 (1999)
  92. Bezerra C G, Albuquerque E L, Jr E N Physica A: Statistical Mechanics And Its Applications 267 124 (1999)
  93. Yu Z-G Physics Letters A 257 221 (1999)
  94. Tarasov S Yu, Kolubaev A V, Lipnitskii A G Tech. Phys. Lett. 25 119 (1999)
  95. Vasconcelos M S, Albuquerque E L, Nogueira E Physica A: Statistical Mechanics And Its Applications 268 165 (1999)
  96. Budnikov E Yu, Kuboev I Yu et al Meas Tech 42 1062 (1999)
  97. Galiyarova N M, Gorin S V, Dontsova L I Materials Research Innovations 3 30 (1999)
  98. Galiyarova N, Korchmaryuk Ya Ferroelectrics 222 389 (1999)
  99. Galiyarova N, Gorin S Ferroelectrics 222 373 (1999)
  100. Zuev L B J Appl Mech Tech Phys 39 462 (1998)
  101. Guk I P Tech. Phys. 43 353 (1998)
  102. Ren F-Ya, Yu Z-G et al Physica A: Statistical Mechanics And Its Applications 246 419 (1997)
  103. Lyubchenko L S, Zapadinskii B I, Lyubchenko M L Molecular Crystals And Liquid Crystals Science And Technology. Section A. Molecular Crystals And Liquid Crystals 305 081 (1997)
  104. Gorobets Yu I, Kuchko A N, Salkov I G Chaos, Solitons & Fractals 8 941 (1997)
  105. Kulish V V Int J Infrared Milli Waves 18 1053 (1997)
  106. Belushkin A V, Ibberson R M, Shuvalov L A Journal Of Molecular Structure: THEOCHEM 374 161 (1996)
  107. Kapustin V, Podolsky D, Mestcherjakov V Electrical Contacts - 1996. Proceedings of the Forty-Second IEEE Holm Conference on Electrical Contacts. Joint with the 18th International Conference on Electrical Contacts, (1996) p. 50
  108. Zverev V V, Zverev V V Teor. Mat. Fiz. 107 3 (1996) [Zverev V V Theor Math Phys 107 419 (1996)]
  109. Belushkin A V, Ibberson R M, Shuvalov L A Journal Of Molecular Structure 374 161 (1996)
  110. Olemskoi A I Uspekhi Fizicheskikh Nauk 166 697 (1996)
  111. Lyubchenko M L, Lyubchenko L S et al Molecular Crystals And Liquid Crystals Science And Technology. Section A. Molecular Crystals And Liquid Crystals 274 205 (1995)
  112. Olemskoi A I Russ Phys J 37 1063 (1994)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions