RSS feeds
РусскийEnglish
Issue 9, 2026
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

Оригинал: Зосимов В В, Лямшев Л М «Фракталы в волновых процессах» УФН 165 361–402 (1995); DOI: 10.3367/UFNr.0165.199504a.0361

References (165) Cited by (74) ↓ Similar articles (20)

  1. Pulido M A P, Sousa J V d C et al Communications In Nonlinear Science And Numerical Simulation 162 110360 (2026)
  2. Grinchuk P S, Danilova-Tretiak S M Chaos, Solitons & Fractals 194 116137 (2025)
  3. Grinchuk P S Vesc?y Akadem?y?y Navuk Belarus?y. Sery?n Fizika-matematyčnyh Navuk 61 (1) 17 (2025)
  4. Mofor I A, Tanekou G B et al Eur. Phys. J. Plus 140 (7) (2025)
  5. Sibatov R T, Golmankhaneh A Kh et al Fractal Fract 6 (2) 115 (2022)
  6. Banakh L Journal Of Sound And Vibration 520 116541 (2022)
  7. Dyskin A V, Pasternak E International Journal Of Engineering Science 149 103244 (2020)
  8. Korolenko P V Phys. Wave Phen. 28 (4) 313 (2020)
  9. Banakh L Vib. Proced. 25 54 (2019)
  10. Kitai M S, Nazarov M M Radiophys Quantum El 61 (5) 374 (2018)
  11. Smolanov N A, Neverov V A Inorg. Mater. Appl. Res. 8 (3) 419 (2017)
  12. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 3 (2016) p. 59
  13. Mvogo A, Tambue A et al Communications In Nonlinear Science And Numerical Simulation 39 396 (2016)
  14. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 4 (2016) p. 141
  15. Pisarenko T A, Frolov A, Kraynova G SSP 215 190 (2014)
  16. Konopleva N G, Ivanyuk G Yu et al Geol. Ore Deposits 56 (7) 576 (2014)
  17. ’Iрі’?ch’?’?’?’? ’E ’n, ’Iрі’?ch’?’?’?’? ’n ’d Vìsn. Nac. Akad. Nauk Ukr. (9) (2013)
  18. Kraynova G S, Frolov A M, Pisarenko T A AMR 718-720 85 (2013)
  19. Vybornov F I, Rakhlin A V Open Astronomy 22 (1) (2013)
  20. Campo F A, Barbero E J Journal Of Non-Crystalline Solids 358 (4) 721 (2012)
  21. Barbero E J, Campo F A Journal Of Non-Crystalline Solids 358 (4) 728 (2012)
  22. Bragin V A, Dushenok S A et al Russ. J. Phys. Chem. B 6 (3) 390 (2012)
  23. Alisultanov Z Z, Meilanov R P Theor Math Phys 171 (3) 769 (2012)
  24. ’B’?’?су’?т’?’?’?’? ’O ’O, Alisultanov Z Z ’? ’?р Teor. Mat. Fiz. 171 (3) 404 (2012)
  25. Campo F A, Murillo J S R, Barbero E J Journal Of Non-Crystalline Solids 357 (10) 2046 (2011)
  26. Rivas M J S, Bachlechner M E et al Journal Of Non-Crystalline Solids 356 (25-27) 1325 (2010)
  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. Barakhtin B K, Savenkov G G J Appl Mech Tech Phy 50 (6) 965 (2009)
  29. Maksimenko V V, Kupriyanov L Yu, Zagainov V A Nanotechnol Russia 4 (11-12) 795 (2009)
  30. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum El 51 (1) 20 (2008)
  31. Barmin Yu V, Bataronov I L et al J. Phys.: Condens. Matter 20 (11) 114117 (2008)
  32. Zhabrev V A, Margolin V I Inorg Mater 44 (13) 1459 (2008)
  33. DROUJININE A, ROK V Fractals 15 (02) 127 (2007)
  34. ’z’?’?’?’?’? ’B ’v, ’B’?’?shch’?’?’?’? ’E ’l Uspekhi Fizicheskikh Nauk 177 (8) 859 (2007)
  35. Dyskin A V Hydrol. Earth Syst. Sci. 11 (2) 665 (2007)
  36. Korabel N, Zaslavsky G M, Tarasov V E Communications In Nonlinear Science And Numerical Simulation 12 (8) 1405 (2007)
  37. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 383 (2) 291 (2007)
  38. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum Electron 50 (4) 274 (2007)
  39. Zhukovsky S V, Chigrin D N, Kroha J J. Opt. Soc. Am. B 23 (10) 2265 (2006)
  40. Dyskin A V Philosophical Magazine 86 (21-22) 3117 (2006)
  41. Tarasov V E, Zaslavsky G M Chaos: An Interdisciplinary Journal of Nonlinear Science 16 (2) (2006)
  42. Tarasov V E, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 11 (8) 885 (2006)
  43. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 368 (2) 399 (2006)
  44. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 354 249 (2005)
  45. Dyskin A V International Journal Of Solids And Structures 42 (2) 477 (2005)
  46. Makara V A, Steblenko L P et al SSP 108-109 339 (2005)
  47. Egerev S V, Ovchinnikov O B, Fokin A V Acoust. Phys. 51 (2) 160 (2005)
  48. Korvin G, Oleschko K Chaos, Solitons & Fractals 19 (2) 421 (2004)
  49. Knebel G, Méasson M-A et al J. Phys.: Condens. Matter 16 (49) 8905 (2004)
  50. Zelenyi L M, Milovanov A V Uspekhi Fizicheskikh Nauk 174 (8) 809 (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. Savenkov G F Journal Of Applied Mechanics And Technical Physics 45 (1) 105 (2004)
  53. Lisovskii F V, Lukashenko L I, Mansvetova E G Jetp Lett. 79 (7) 352 (2004)
  54. Weitzner H, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 8 (3-4) 273 (2003)
  55. Oleschko K, Korvin G et al Phys. Rev. E 67 (4) (2003)
  56. Boadu F K Geophysical Journal International 155 (2) 557 (2003)
  57. 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
  58. Abramenko V I Astron. Rep. 46 (2) 161 (2002)
  59. Meilanov R P, Yanpolov M S Tech. Phys. Lett. 28 (1) 30 (2002)
  60. Casari C S, Li B A et al Phys. Rev. B 64 (8) (2001)
  61. Bottani C E Nanostructured Carbon for Advanced Applications Chapter 7 (2001) p. 149
  62. Zakharov K A, Meilanov R P Radiophysics And Quantum Electronics 44 (8) 653 (2001)
  63. Qian Z W The Journal of the Acoustical Society of America 107 (1) 260 (2000)
  64. Akishin P G, Altaisky M V et al Chaos, Solitons & Fractals 11 (1-3) 207 (2000)
  65. Uchaikin V V, Korobko D A Tech. Phys. Lett. 25 (6) 435 (1999)
  66. Galiyarova N M, Gorin S V, Dontsova L I Materials Research Innovations 3 (1) 30 (1999)
  67. Galiyarova N Ferroelectrics 222 (1) 381 (1999)
  68. (SEG Technical Program Expanded Abstracts 1998) Vol. SEG Technical Program Expanded Abstracts 1998Evidence of scaling for acoustic waves in multiscale media and its possible implicationsFelix J.Herrmann1 (1998) p. 1684
  69. Osipov V Yu Tech. Phys. 43 (9) 1075 (1998)
  70. Akishin P G, Altaisky M V et al IFAC Proceedings Volumes 31 (20) 907 (1998)
  71. Uchaikin V V, Gusarov G G, Korobko D A J Math Sci 92 (3) 3940 (1998)
  72. Nigmatullin R R, Ryabov Ya E Russ Phys J 40 (4) 314 (1997)
  73. Zosimov V V, Tarasov D N J. Exp. Theor. Phys. 84 (4) 725 (1997)
  74. Kistenev Yu V, Shapovalov A V Russ Phys J 39 (5) 435 (1996)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions