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 velocityv i(x j,t) and stochastic velocityu i(x j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv i(x j,t) in the caseu i →0. In the limit l →0, these equations acquire the Newtonian form.
Similar content being viewed by others
References
G. I. Sivashinsky,Found. Phys. 8, 735 (1978).
G. I. Sivashinksky,Acta Astronautica 4, 1177 (1977); D. M. Michelson and G. I. Sivashinsky,Acta Astronautica 4, 1207 (1977).
Kh. Namsrai, Preprint JINR, E2-12760, Dubna (1979);Found. Phys., to be published.
E. Nelson, Dynamical Theories of Brownian Motion (Princeton, New Jersey, 1967);
L. de la Peña Auerbach and A. M. Cetto,Found. Phys. 5, 355 (1975);
B. Skagerstam, Inst. Theor. Phys. report 75-21, Gothenburg, Sweden (1975).
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).
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).
D. I. Blokhinstev, [Sov. J. Part. Nucl. 5, 242 (1975)].Fiz. Elem. Chastits At. Yad. 5, 606 (1975).
C. Frederick,Phys. Rev. D 13, 3183 (1976).
S. Roy,Nuovo Cim. 51, 29 (1979).
E. Prugovecki,Phys. Rev. D 18, 3655 (1978);J. Math. Phys. 19, 2260, 2271 (1978).
D. Kershaw,Phys. Rev. 136, B1850 (1964).
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).
M. Davidson,J. Math. Phys. 19, 1975 (1978).
F. Guerra and P. Ruggiero,Lett. Nuovo Cim. 23, 529 (1978).
J. P. Vigier,Lett. Nuovo Cim. 24, 265 (1979).
Ch. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973).
W. J. Lehr and J. L. Park,J. Math. Phys. 18, 1235 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Namsrai, K. A stochastic derivation of the Sivashinsky equation for the self-turbulent motion of a free particle. Found Phys 10, 731–742 (1980). https://doi.org/10.1007/BF00708419
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00708419