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 is available at IOP
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/
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 (64) ↓ Similar articles (20)

  1. Dyskin A V, Pasternak E International Journal Of Engineering Science 149 103244 (2020)
  2. Banakh L 25 54 (2019)
  3. Kitai M S, Nazarov M M Radiophys Quantum El 61 374 (2018)
  4. Smolanov N A, Neverov V A Inorg. Mater. Appl. Res. 8 419 (2017)
  5. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 4 (2016) p. 141
  6. Janahmadov A Kh, Javadov M Y Synergetics and Fractals in Tribology Materials Forming, Machining And Tribology Chapter 3 (2016) p. 59
  7. Mvogo A, Tambue A et al Communications In Nonlinear Science And Numerical Simulation 39 396 (2016)
  8. Pisarenko T A, Frolov A, Kraynova G SSP 215 190 (2014)
  9. Konopleva N G, Ivanyuk G Yu et al Geol. Ore Deposits 56 576 (2014)
  10. Vybornov F I, Rakhlin A V 22 (1) (2013)
  11. Kraynova G S, Frolov A M, Pisarenko T A AMR 718-720 85 (2013)
  12. Grinchenko V T, Grinchenko T A Visn. Nac. Akad. Nauk Ukr (9) 53 (2013)
  13. Bragin V A, Dushenok S A et al Russ. J. Phys. Chem. B 6 390 (2012)
  14. Barbero E J, Campo F A Journal Of Non-Crystalline Solids 358 728 (2012)
  15. Alisultanov Z Z, Alisultanov Z Z i dr Teor. Mat. Fiz. 171 404 (2012) [Alisultanov Z Z, Meilanov R P Theor Math Phys 171 769 (2012)]
  16. Campo F A, Barbero E J Journal Of Non-Crystalline Solids 358 721 (2012)
  17. Campo F A, Murillo J S R, Barbero E J Journal Of Non-Crystalline Solids 357 2046 (2011)
  18. Rivas M J S, Bachlechner M E et al Journal Of Non-Crystalline Solids 356 1325 (2010)
  19. Dyskin A V, Pasternak E Iutam Bookseries Vol. IUTAM Symposium on Scaling in Solid Mechanics10 Chapter 18 (2009) p. 189
  20. Barakhtin B K, Savenkov G G J Appl Mech Tech Phy 50 965 (2009)
  21. Maksimenko V V, Kupriyanov L Yu, Zagainov V A Nanotechnol Russia 4 795 (2009)
  22. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum El 51 20 (2008)
  23. Zhabrev V A, Margolin V I Inorg Mater 44 1459 (2008)
  24. Barmin Yu V, Bataronov I L et al J. Phys.: Condens. Matter 20 114117 (2008)
  25. Korabel N, Zaslavsky G M, Tarasov V E Communications In Nonlinear Science And Numerical Simulation 12 1405 (2007)
  26. Pavlov A N, Anishchenko V S Uspekhi Fizicheskikh Nauk 177 859 (2007)
  27. DROUJININE ALEXANDER, ROK VLADIMIR Fractals 15 127 (2007)
  28. Alimov V A, Vybornov F I, Rakhlin A V Radiophys Quantum Electron 50 274 (2007)
  29. Dyskin A V Hydrol. Earth Syst. Sci. 11 665 (2007)
  30. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 383 291 (2007)
  31. Tarasov V E, Zaslavsky G M Chaos 16 023110 (2006)
  32. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 368 399 (2006)
  33. Dyskin A V Philosophical Magazine 86 3117 (2006)
  34. Zhukovsky S V, Chigrin D N, Kroha J J. Opt. Soc. Am. B 23 2265 (2006)
  35. Tarasov V E, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 11 885 (2006)
  36. Dyskin A V International Journal Of Solids And Structures 42 477 (2005)
  37. Tarasov V E, Zaslavsky G M Physica A: Statistical Mechanics And Its Applications 354 249 (2005)
  38. Egerev S V Acoust. Phys. 51 160 (2005)
  39. Makara V A, Steblenko L P et al SSP 108-109 339 (2005)
  40. Knebel G, Méasson M-A et al J. Phys.: Condens. Matter 16 8905 (2004)
  41. Zelenyi L M, Milovanov A V Uspekhi Fizicheskikh Nauk 174 809 (2004)
  42. Lisovskii F V, Lukashenko L I, Mansvetova E G Jetp Lett. 79 352 (2004)
  43. Korvin G, Oleschko K Chaos, Solitons & Fractals 19 421 (2004)
  44. 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
  45. Boadu F K 155 557 (2003)
  46. Oleschko K, Korvin G et al Phys. Rev. E 67 (4) (2003)
  47. Weitzner H, Zaslavsky G M Communications In Nonlinear Science And Numerical Simulation 8 273 (2003)
  48. Meilanov R P, Yanpolov M S Tech. Phys. Lett. 28 30 (2002)
  49. Dyskin A V Solid Mechanics And Its Applications Vol. IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials97 Chapter 10 (2002) p. 73
  50. Abramenko V I Astron. Rep. 46 161 (2002)
  51. Bottani C E Nanostructured Carbon for Advanced Applications Chapter 7 (2001) p. 149
  52. Casari C S, Li B A et al Phys. Rev. B 64 (8) (2001)
  53. Qian Z W The Journal Of The Acoustical Society Of America 107 260 (2000)
  54. Akishin P G, Altaisky M V et al Chaos, Solitons & Fractals 11 207 (2000)
  55. Galiyarova N M, Gorin S V, Dontsova L I Materials Research Innovations 3 30 (1999)
  56. Galiyarova N Ferroelectrics 222 381 (1999)
  57. Uchaikin V V, Korobko D A Tech. Phys. Lett. 25 435 (1999)
  58. Uchaikin V V, Gusarov G G, Korobko D A J Math Sci 92 3940 (1998)
  59. Akishin P G, Altaisky M V et al IFAC Proceedings Volumes 31 907 (1998)
  60. Osipov V Yu Tech. Phys. 43 1075 (1998)
  61. Herrmann F J SEG Technical Program Expanded Abstracts 1998, (1998) p. 1684
  62. Nigmatullin R R, Ryabov Ya E Russ Phys J 40 314 (1997)
  63. Zosimov V V, Tarasov D N J. Exp. Theor. Phys. 84 725 (1997)
  64. Kistenev Yu V, Shapovalov A V Russ Phys J 39 435 (1996)

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions