RSS feeds
ÐóññêèéEnglish
Issue 12, 2025
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1995

 / 

April

←  →

Reviews of topical problems


Fractals in wave processes

 a,  b
a Research Institute of Applied Acoustics, Dubna, Moscow Region, Russian Federation
b N.N. Andreev Acoustics Institute, Russian Academy of Sciences, ul. Shvernika 4, Moscow, 117036, Russian Federation

A review of fundamental results on fractal structure manifestation in wave processes is presented. Elastic properties and dispersion of fractal materials are discussed; their distribution density, and the shape of wave functions of their localised elastic oscillations, fractons. Examples of their application for the explanation of amorphic properties of solids are presented. Patterns of wave scattering and emission by fractal structures are examined. Principal methods of random signal analysis employed to reveal different fractal structures associated with these signals are described. Data on fractal properties of wave fields are discussed.

Fulltext pdf (1.1 MB)
Fulltext is also available at DOI: 10.1070/PU1995v038n04ABEH000080
PACS: 47.35.+i, 47.52.+j, 47.53.+n, 61.43.Hv (all)
DOI: 10.1070/PU1995v038n04ABEH000080
URL: https://ufn.ru/en/articles/1995/4/a/
A1995RH54700001
Citation: Zosimov V V, Lyamshev L M "Fractals in wave processes" Phys. Usp. 38 347–384 (1995)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Çîñèìîâ Â Â, Ëÿìøåâ Ë Ì «Ôðàêòàëû â âîëíîâûõ ïðîöåññàõ» ÓÔÍ 165 361–402 (1995); DOI: 10.3367/UFNr.0165.199504a.0361

References (165) Cited by (72) ↓ Similar articles (20)

  1. Grinchuk P S Vescì Akademìì Navuk Belarusì. Seryâ Fizika-matematyčnyh Navuk 61 (1) 17 (2025)
  2. Grinchuk P S, Danilova-Tretiak S M Chaos, Solitons & Fractals 194 116137 (2025)
  3. Mofor I A, Tanekou G B et al Eur. Phys. J. Plus 140 (7) (2025)
  4. Sibatov R T, Golmankhaneh A Kh et al Fractal Fract 6 (2) 115 (2022)
  5. Banakh L Journal Of Sound And Vibration 520 116541 (2022)
  6. Korolenko P V Phys. Wave Phen. 28 (4) 313 (2020)
  7. Dyskin A V, Pasternak E International Journal Of Engineering Science 149 103244 (2020)
  8. Banakh L Vib. Proced. 25 54 (2019)
  9. Kitai M S, Nazarov M M Radiophys Quantum El 61 (5) 374 (2018)
  10. Smolanov N A, Neverov V A Inorg. Mater. Appl. Res. 8 (3) 419 (2017)
  11. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 3 (2016) p. 59
  12. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 4 (2016) p. 141
  13. Mvogo A, Tambue A et al Communications In Nonlinear Science And Numerical Simulation 39 396 (2016)
  14. Konopleva N G, Ivanyuk G Yu et al Geol. Ore Deposits 56 (7) 576 (2014)
  15. Pisarenko T A, Frolov A, Kraynova G SSP 215 190 (2014)
  16. Gr³nchenko V T, Gr³nchenko T O Vìsn. Nac. Akad. Nauk Ukr. (9) (2013)
  17. Vybornov F I, Rakhlin A V Open Astronomy 22 (1) (2013)
  18. Kraynova G S, Frolov A M, Pisarenko T A AMR 718-720 85 (2013)
  19. Alisultanov Z Z, Alisultanov Z Z i dr Teor. Mat. Fiz. 171 (3) 404 (2012) [Alisultanov Z Z, Meilanov R P Theor Math Phys 171 (3) 769 (2012)]
  20. Bragin V A, Dushenok S A et al Russ. J. Phys. Chem. B 6 (3) 390 (2012)
  21. Barbero E J, Campo F A Journal Of Non-Crystalline Solids 358 (4) 728 (2012)
  22. Campo F A, Barbero E J Journal Of Non-Crystalline Solids 358 (4) 721 (2012)
  23. Campo F A, Murillo J S R, Barbero E J Journal Of Non-Crystalline Solids 357 (10) 2046 (2011)
  24. Rivas M J S, Bachlechner M E et al Journal Of Non-Crystalline Solids 356 (25-27) 1325 (2010)
  25. Maksimenko V V, Kupriyanov L Yu, Zagainov V A Nanotechnol Russia 4 (11-12) 795 (2009)
  26. Barakhtin B K, Savenkov G G J Appl Mech Tech Phy 50 (6) 965 (2009)
  27. Dyskin A V, Pasternak E Iutam Bookseries Vol. IUTAM Symposium on Scaling in Solid MechanicsScaling of Effective Moduli of Generalised Continua10 Chapter 18 (2009) p. 189
  28. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum El 51 (1) 20 (2008)
  29. Zhabrev V A, Margolin V I Inorg Mater 44 (13) 1459 (2008)
  30. Barmin Yu V, Bataronov I L et al J. Phys.: Condens. Matter 20 (11) 114117 (2008)
  31. Korabel N, Zaslavsky G M, Tarasov V E Communications In Nonlinear Science And Numerical Simulation 12 (8) 1405 (2007)
  32. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 383 (2) 291 (2007)
  33. Pavlov A N, Anishchenko V S Uspekhi Fizicheskikh Nauk 177 (8) 859 (2007)
  34. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum Electron 50 (4) 274 (2007)
  35. DROUJININE ALEXANDER, ROK VLADIMIR Fractals 15 (02) 127 (2007)
  36. Dyskin A V Hydrol. Earth Syst. Sci. 11 (2) 665 (2007)
  37. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 368 (2) 399 (2006)
  38. Tarasov V E, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 11 (8) 885 (2006)
  39. Tarasov V E, Zaslavsky G M Chaos: An Interdisciplinary Journal of Nonlinear Science 16 (2) (2006)
  40. Zhukovsky S V, Chigrin D N, Kroha J J. Opt. Soc. Am. B 23 (10) 2265 (2006)
  41. Dyskin A V Philosophical Magazine 86 (21-22) 3117 (2006)
  42. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 354 249 (2005)
  43. Makara V A, Steblenko L P et al SSP 108-109 339 (2005)
  44. Egerev S V Acoust. Phys. 51 (2) 160 (2005)
  45. Dyskin A V International Journal Of Solids And Structures 42 (2) 477 (2005)
  46. Korvin G, Oleschko K Chaos, Solitons & Fractals 19 (2) 421 (2004)
  47. Lisovskii F V, Lukashenko L I, Mansvetova E G Jetp Lett. 79 (7) 352 (2004)
  48. Knebel G, Méasson M-A et al J. Phys.: Condens. Matter 16 (49) 8905 (2004)
  49. Zelenyi L M, Milovanov A V Uspekhi Fizicheskikh Nauk 174 (8) 809 (2004)
  50. Savenkov G F Journal Of Applied Mechanics And Technical Physics 45 (1) 105 (2004)
  51. Vol. Proceedings. The 8th Russian-Korean International Symposium on Science and Technology, 2004. KORUS 2004.Localization and crossover on fractal gridsA.N.BondarenkoV.A.Levin2 (2004) p. 106
  52. Boadu F K Geophysical Journal International 155 (2) 557 (2003)
  53. Oleschko K, Korvin G et al Phys. Rev. E 67 (4) (2003)
  54. Weitzner H, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 8 (3-4) 273 (2003)
  55. Meilanov R P, Yanpolov M S Tech. Phys. Lett. 28 (1) 30 (2002)
  56. Dyskin A V Solid Mechanics And Its Applications Vol. IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous MaterialsMechanics of Fractal Materials97 Chapter 10 (2002) p. 73
  57. Abramenko V I Astron. Rep. 46 (2) 161 (2002)
  58. Zakharov K A, Meilanov R P Radiophysics And Quantum Electronics 44 (8) 653 (2001)
  59. Bottani C E Nanostructured Carbon for Advanced Applications Chapter 7 (2001) p. 149
  60. Casari C S, Li B A et al Phys. Rev. B 64 (8) (2001)
  61. Qian Z W The Journal of the Acoustical Society of America 107 (1) 260 (2000)
  62. Akishin P G, Altaisky M V et al Chaos, Solitons & Fractals 11 (1-3) 207 (2000)
  63. Galiyarova N M, Gorin S V, Dontsova L I Materials Research Innovations 3 (1) 30 (1999)
  64. Galiyarova N Ferroelectrics 222 (1) 381 (1999)
  65. Uchaikin V V, Korobko D A Tech. Phys. Lett. 25 (6) 435 (1999)
  66. Uchaikin V V, Gusarov G G, Korobko D A J Math Sci 92 (3) 3940 (1998)
  67. Akishin P G, Altaisky M V et al IFAC Proceedings Volumes 31 (20) 907 (1998)
  68. Osipov V Yu Tech. Phys. 43 (9) 1075 (1998)
  69. Herrmann F J SEG Technical Program Expanded Abstracts 1998, (1998) p. 1684
  70. Zosimov V V, Tarasov D N J. Exp. Theor. Phys. 84 (4) 725 (1997)
  71. Nigmatullin R R, Ryabov Ya E Russ Phys J 40 (4) 314 (1997)
  72. Kistenev Yu V, Shapovalov A V Russ Phys J 39 (5) 435 (1996)
© 1918–2025 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions