Issues

 / 

2004

 / 

August

  

Methodological notes


Classical mechanical analogs of relativistic effects

,
Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina, 4, Moscow, 119991, Russian Federation

The analogs of relativistic effects in classical mechanics, which are observed in the propagation of solitons in solids, are discussed. These effects are described by formulas similar to those of the special theory of relativity, with the speed of sound entering them in lieu of the speed of light. These parallels are shown to be a part of the correspondence between the soliton theory and field theories (in particular, electrodynamics). The effect of Lorentz-invariance breakdown in mechanical systems on dynamic soliton properties is considered. It is shown that supersonic solitons (in particular, dislocations) can propagate in such systems.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 03.30.+p, 05.45.Yv, 11.15.−q, 61.72.Lk (all)
DOI: 10.1070/PU2004v047n08ABEH001402
URL: https://ufn.ru/en/articles/2004/8/c/
Citation: Musienko A I, Manevich L I "Classical mechanical analogs of relativistic effects" Phys. Usp. 47 797–820 (2004)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Мусиенко А И, Маневич Л И «Аналоги релятивистских эффектов в классической механике» УФН 174 861–886 (2004); DOI: 10.3367/UFNr.0174.200408c.0861

References (85) ↓ Cited by (8) Similar articles (20)

  1. Lamb G L (Jr) Elements of Soliton Theory (New York: Wiley, 1980) [Translated into Russian (Moscow: Mir, 1983)]
  2. Hirth J P, Lothe J Theory of Dislocations (New York: McGraw-Hill, (1968) [Translated into Russian (Moscow: Atomizdat, 1972)]
  3. Kosevich A M Usp. Fiz. Nauk 84 579 (1964) [Sov. Phys. Usp. 7 837 (1964)]
  4. Musienko A I, Koptsik V A Kristallografiya 40 438 (1995) [Crystallogr. Rep. 40 398 (1995)]
  5. Kadić A, Edelen D G B A Gauge Theory of Dislocations and Disclinations (Berlin: Springer-Verlag, 1983) [Translated into Russian (Moscow: Mir, 1987)]
  6. Takhtadzhyan L A, Faddeev L D Gamil’tonov Podkhod v Teorii Solitonov (Moscow: Nauka, 1986) [Translated into English: Faddeev L D, Takhtajan L A Hamiltonian Methods in the Theory of Solitons (Berlin: Springer-Verlag, 1987)]
  7. Zakharov V E, Malomed B A, in Fizicheskaya Entsiklopediya (Encyclopedia of Physics) Vol. 4 (Editor-in-Chief A M Prokhorov, Moscow: Bol’shaya Rossiiskaya Entsiklopediya, 1994) p. 571
  8. Mermin N D Rev. Mod. Phys. 51 591 (1979)
  9. Monastyrsky M I Topology of Gauge Fields and Condensed Matter (New York: Plenum Press, 1993) [Translated into Russian (Moscow: PAIMS, 1995)]
  10. Landau L D, Lifshitz E M Teoriya Uprugosti (Theory of Elasticity, Moscow: Nauka, 1987) [Translated into English (Oxford: Pergamon Press, 1986)]
  11. Ablowitz M J, Segur H Solitons and the Inverse Scattering Transform (Philadelphia, Pa.: SIAM, 1981) [Translated into Russian (Moscow: Mir, 1987)]
  12. Petviashvili V I, Pokhotelov O A Uedinennye Volny v Plazme i Atmosfere (Solitary Waves in Plasmas and in the Atmosphere, Moscow: Energoatomizdat, 1989) [Translated into English (Philadelphia, Pa.: Gordon and Breach Sci. Publ., 1992)]
  13. Davydov A S Solitony v Molekulyarnykh Sistemakh (Solitons in Molecular Systems, Kiev: Naukova Dumka, 1984) [Translated into English (Dordrecht: D. Reidel, 1991)]
  14. Volovik G E Phys. Rep. 351 195 (2001)
  15. Rajaraman R Solitons and Instantons: an Introduction to Solitons and Instantons in Quantum Field Theory (Amsterdam: North-Holland Publ. Co., 1982) [Translated into Russian (Moscow: Mir, 1985)]
  16. Scott A Phys. Rep. 217 1 (1992)
  17. Yakushevich L V Nonlinear Physics of DNA (Chichester: John Wiley & Sons, 1998)
  18. Lakhno V D J. Biol. Phys. 26 133 (2000)
  19. Mornev O A, Aslanidi O V, Tsyganov I M Macromol. Symp. 160 115 (2000)
  20. Scott A C Active and Nonlinear Wave Propagation in Electronics (New York: Wiley-Intersci., 1970) [Translated into Russian (Moscow: Sov. Radio, 1977)]
  21. Zubova E A, Balabaev N K, Manevich L I Zh. Eksp. Teor. Fiz. 115 1063 (1999) [JETP 88 586 (1999)]
  22. Zubova E A et al. Zh. Eksp. Teor. Fiz. 118 592 (2000) [JETP 91 515 (2000)]
  23. Savin A V, Manevitch L I Phys. Rev. E 61 7065 (2000)
  24. Savin A V, Manevitch L I Phys. Rev. B 63 224303 (2001)
  25. Gardner C S et al. Phys. Rev. Lett. 19 1095 (1967)
  26. Toda M J. Phys. Soc. Jpn. 22 431 (1967)
  27. Toda M J. Phys. Soc. Jpn. 23 501 (1967)
  28. Toda M Theory of Nonlinear Lattices (Berlin: Springer-Verlag, 1981) [Translated into Russian (Moscow: Mir, 1984)]
  29. Cenian A, Gabriel H J. Phys.: Condens. Matter 13 4323 (2001)
  30. Narayanamurti V, Varma C M Phys. Rev. Lett. 25 1105 (1970)
  31. Astakhova T Yu et al. Phys. Rev. B 64 035418 (2001)
  32. Collins M A, in Advances in Chemical Physics Vol. 53 (Eds I Prigogine, S A Rice, New York: John Wiley & Sons, 1983) p. 225
  33. Pnevmatikos St C.R. Acad. Sci. Ser. II (Paris) 296 1031 (1983)
  34. Balabaev N K, Gendel’man O V, Manevich L I, in Problemy Nelineinoi Mekhaniki i Fiziki Materialov (Problems in Nonlinear Mechanics and Material Physics, Ed. L I Manevich, Dnepropetrovsk: RIK NGA Ukrainy, 1999) p. 37
  35. Balabaev N K, Gendelman O V, Manevitch L I Phys. Rev. E 64 036702 (2001)
  36. Manevich L I, Savin A V Vysokomol. Soedin., Ser. A 38 1209 (1996) [Polymer Sci. A 38 789 (1996)]
  37. Manevitch L I, Savin A V Phys. Rev. E 55 4713 (1997)
  38. Remoissenet M, Flytzanis N J. Phys. C: Solid State Phys. 18 1573 (1985)
  39. Nesterenko V F Zh. Prikl. Mekh. Tekh. Fiz. 24 (5) 136 (1983) [J. Appl. Mech. Tech. Phys. 5 733 (1983)]
  40. Lazaridi A N, Nesterenko V F Zh. Prikl. Mekh. Tekh. Fiz. 26 (3) 115 (1985) [J. Appl. Mech. Tech. Phys. 26 405 (1985)]
  41. Coste C, Falcon E, Fauve S Phys. Rev. E 56 6104 (1997)
  42. Batteh J H, Powell J D, in Solitons in Action (Eds K Lonngren, A Scott, New York: Academic Press, 1978) [Translated into Russian (Moscow: Mir, 1981) p. 269]
  43. Peyrard M et al. Phys. Rev. B 33 2350 (1986)
  44. Ostrovsky L A, Potapov A I Modulated Waves: Theory and Applications (Baltimore, Md.: The Johns Hopkins Univ. Press, 1999)
  45. Erofeev V I, Kazhaev V V, Semerikova N P Volny v Sterzhnyakh: Dispersiya, Dissipatsiya, Nelineinost’ (Waves in Rods: Dispersion, Dissipation, Nonlinearity, Moscow: Fizmatlit, 2002)
  46. Dreiden G V et al. Zh. Tekh. Fiz. 58 2040 (1988) [Sov. Phys. Tech. Phys. 33 1237 (1988)]
  47. Samsonov A M et al. Phys. Rev. B 57 5778 (1998)
  48. Sharon E, Cohen G, Fineberg J Phys. Rev. Lett. 88 085503 (2002)
  49. Savin A V Zh. Eksp. Teor. Fiz. 108 1105 (1995) [JETP 81 608 (1995)]
  50. Kosevich A M, Kovalev A S Solid State Commun. 12 763 (1973)
  51. Zolotaryuk Y, Eilbeck J C, Savin A V Physica D 108 81 (1997)
  52. Braun O M Phys. Rev. E 62 7315 (2000)
  53. Zolotaryuk A V, Pnevmatikos St, Savin A V Physica D 51 407 (1991)
  54. Pnevmatikos St, Tsironis G P, Zolotaryuk A V J. Mol. Liq. 41 85 (1989)
  55. Nagle J F, Tristram-Nagle S J. Membrane Biol. 74 1 (1983)
  56. Manevich L I et al. Usp. Fiz. Nauk 164 937 (1994) [Phys. Usp. 37 859 (1994)]
  57. Manevitch L I, Smirnov V V Phys. Lett. A 165 427 (1992)
  58. Enikolopian N S, Manevitch L I, Smirnov V V Khim. Fiz. 10 389 (1991) [Sov. J. Chem. Phys. 10 587 (1992)]
  59. Manevich L I, Smirnov V V J. Phys.: Condens. Matter 7 255 (1995)
  60. Manevich L I, Smirnov V V, in Chemistry Reviews Vol. 23, Pt. 2 (Eds P Yu Butyagin, A M Dubinskaya, Amsterdam: Harwood Acad. Publ., 1998) p. 1
  61. Wang L J, Kuzmich A, Dogariu A Nature 406 277 (2000)
  62. Sazonov S V Usp. Fiz. Nauk 171 663 (2001) [Phys. Usp. 44 631 (2001)]
  63. Mirkin L I Fizicheskie Osnovy Prochnosti i Plastichnosti (The Physical Foundations of Strength and Plasticity, Moscow: Izd. MGU, 1968)
  64. Weertman J, Weertman J R, in Dislocations in Solids Vol. 3 (Ed. F R N Nabarro, Amsterdam: North-Holland Publ. Co., 1980) p. 1
  65. Fushchich V I, Nakonechnyi V V Ukr. Mat. Zh. 32 267 (1980)
  66. Mura T Philos. Mag.8 843 (1963)
  67. Mura T Micromechanics of Defects in Solids 2nd ed. (Dordrecht: M. Nijhoff, 1987)
  68. Hoover W G, Hoover N E, Moss W C Phys. Lett. A 63 324 (1977)
  69. Gumbsch P, Gao H Science 283 965 (1999)
  70. Shi S Q, Huang H, Woo C H Comp. Mater. Sci. 23 95 (2002)
  71. Koizumi H, Kirchner H O K, Suzuki T Phys. Rev. B 65 214104 (2002)
  72. Rosakis P Phys. Rev. Lett. 86 95 (2001)
  73. de Wit R J. Res. NBS A: Phys. Chem. 77 49, 359, 607 (1973) [Translated into Russian: de Wit R Kontinual’naya Teoriya Disklinatsii (Continuous Theory of Disclinations, Moscow: Mir, 1977)]
  74. de Wit R J. Res. NBS A: Phys. Chem. 77 49 (1973)
  75. Kossecka E, de Wit R Arch. Mech. Stosowanej 29 749 (1977)
  76. Nelson D R, in Fundamental Problems in Statistical Mechanics Vol. 5 (Ed. E G D Cohen, Amsterdam: North-Holland, 1980) p. 53
  77. Menskii M B Gruppa Putei: Izmereniya, Polya, Chastitsy (Path Group: Measurements. Fields. Particles, Moscow: Nauka, 1983)
  78. Günther H Z. Angew. Math. Mech. 56 429 (1976)
  79. Musienko A I, Koptsik V A Kristallografiya 41 586 (1996) [Crystallogr. Rep. 41 550 (1996)]
  80. Kröner E, in Physics of Defects, Les Houches Session XXXV (Eds R Balian, M Kléman, J-P Poirier, Amsterdam: North-Holland, 1981) p. 215
  81. Hehl F W, McCrea J D Found. Phys. 16 267 (1986)
  82. Katanaev M O, Volovich I V Ann. Phys. (New York) 216 1 (1992)
  83. Ponomarev V N, Barvinskii A O, Obukhov Yu N Geometrodinamicheskie Metody i Kalibrovochnyi Podkhod k Teorii Gravitatsionnykh Vzaimodeistvii (Geometric-Dynamic Methods and Gauge Approach to the Theory of Gravitational Interactions, Moscow: Energoatomizdat, 1985)
  84. Hehl F W et al. Rev. Mod. Phys. 48 393 (1976)
  85. Rybakov Yu P, Sanyuk V I Mnogomernye Solitony: Vvedenie v Teoriyu i Prilozheniya (Multidimensional Solitons: Introduction to the Theory and Applications, Moscow: Izd. RUDN, 2001)

© 1918–2019 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions