Foundations of Physics

, Volume 10, Issue 9–10, pp 731–742 | Cite as

A stochastic derivation of the Sivashinsky equation for the self-turbulent motion of a free particle

  • Kh. Namsrai
Article

Abstract

Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityvi(xj,t) and stochastic velocityui(xj,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forvi(xj,t) in the caseui0. In the limit l →0, these equations acquire the Newtonian form.

Keywords

Relativistic Equation Quadratic Term Free Particle Spatial Stochasticity Hydrodynamical Type 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. I. Sivashinsky,Found. Phys. 8, 735 (1978).Google Scholar
  2. 2.
    G. I. Sivashinksky,Acta Astronautica 4, 1177 (1977); D. M. Michelson and G. I. Sivashinsky,Acta Astronautica 4, 1207 (1977).Google Scholar
  3. 3.
    Kh. Namsrai, Preprint JINR, E2-12760, Dubna (1979);Found. Phys., to be published.Google Scholar
  4. 4. (a)
    E. Nelson, Dynamical Theories of Brownian Motion (Princeton, New Jersey, 1967);Google Scholar
  5. 4. (b)
    L. de la Peña Auerbach and A. M. Cetto,Found. Phys. 5, 355 (1975);Google Scholar
  6. 4. (c)
    B. Skagerstam, Inst. Theor. Phys. report 75-21, Gothenburg, Sweden (1975).Google Scholar
  7. 5.
    S. M. Moore,Found. Phys. 9, 237 (1979); E. Sandos,Nuov. Cim. 19 B, 57 (1973); T. H. Boyer,Phys. Rev. D 11, 790, 809 (1975); M. Surdin,Ann. Inst. H. Poincaré 15, 203 (1971);Found. Phys. 8, 341 (1978).Google Scholar
  8. 6.
    A. March,Z. Phys. 104, 93, 161 (1934);105, 620 (1937); M. A. Markov,Hypersons and K-Mesons (Fizmatgiz, Moscow, 1958) (in Russian); H. Yukawa, Research Inst. Fund. Phys., Kyoto Univ., PIEP-55 (1966).Google Scholar
  9. 7.
    D. I. Blokhinstev, [Sov. J. Part. Nucl. 5, 242 (1975)].Fiz. Elem. Chastits At. Yad. 5, 606 (1975).Google Scholar
  10. 8.
    C. Frederick,Phys. Rev. D 13, 3183 (1976).Google Scholar
  11. 9.
    S. Roy,Nuovo Cim. 51, 29 (1979).Google Scholar
  12. 10.
    E. Prugovecki,Phys. Rev. D 18, 3655 (1978);J. Math. Phys. 19, 2260, 2271 (1978).Google Scholar
  13. 11.
    D. Kershaw,Phys. Rev. 136, B1850 (1964).Google Scholar
  14. 12.
    G. V. Efimov,Commun. Math. Phys. 7, 138 (1968);Nonlocal Interactions of Quantized Fields (Nauka, Moscow, 1977) (in Russian); V. A. Alebastrov and G. V. Efimov,Commun. Math. Phys. 38, 11 (1974).Google Scholar
  15. 13.
    M. Davidson,J. Math. Phys. 19, 1975 (1978).Google Scholar
  16. 14.
    F. Guerra and P. Ruggiero,Lett. Nuovo Cim. 23, 529 (1978).Google Scholar
  17. 15.
    J. P. Vigier,Lett. Nuovo Cim. 24, 265 (1979).Google Scholar
  18. 16.
    Ch. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973).Google Scholar
  19. 17.
    W. J. Lehr and J. L. Park,J. Math. Phys. 18, 1235 (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Kh. Namsrai
    • 1
  1. 1.Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaUSSR

Personalised recommendations