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Russian Physics Journal

, Volume 50, Issue 3, pp 275–282 | Cite as

Application of density functional theory to relativistic hydrodynamics

  • O. Yu. Dinariev
Elementary Particle Physics and Field Theory
  • 29 Downloads

Abstract

The density functional method is used in nonrelativistic hydrodynamics for a description of multicomponent multiphase mixtures. The method is based on an expression for the entropy in the form of a functional with terms quadratic in gradients of component densities. In the present work, the density functional theory is generalized to the relativistic case. This generalization involves a solution of a number of problems: relativistically covariant formulation of the theory equations, derivation of basic relationships with allowance for the generalized relativistic principle of entropy production, and check of the relativistic causality of the theory. It is demonstrated that higher-order derivatives in the theory appear to be compatible with the causality in the basic relationships nonlocal in space and time.

Keywords

Density Functional Theory Entropy Production Energy Momentum Tensor Diffusion Flow Basic Relationship 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    O. Yu. Dinariev, Prikl. Mat. Mekh., 59, No. 5, 776 (1995).Google Scholar
  2. 2.
    O. Yu. Dinariev, Prikl. Mat. Mekh, 62, No. 3, 433 (1998).Google Scholar
  3. 3.
    O. Yu. Dinariev, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 144 (1999).Google Scholar
  4. 4.
    O. Yu. Dinariev, Prikl. Mat. Teor. Fiz., 44, No. 1, 101 (2003).zbMATHGoogle Scholar
  5. 5.
    A. Yu. Dem’yanov and O. Yu. Dinariev, Prikl. Mat. Teor. Fiz., 45, No. 5, 68 (2004).zbMATHGoogle Scholar
  6. 6.
    A. Yu. Dem’yanov and O. Yu. Dinariev, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 101 (2004).Google Scholar
  7. 7.
    O. Yu. Dinariev and N. V. Evseev, Inzh. Fiz. Zh., 78, No. 3, 61 (2005).Google Scholar
  8. 8.
    O. Yu. Dinariev, Russ. Phys. J., No. 9, 713–717 (2000).Google Scholar
  9. 9.
    M.-A. Tonnela, in: Fundamentals of Electromagnetism and Relativity Theory [Russian translation], Inostrannaya Literatura, Moscow (1962).Google Scholar
  10. 10.
    G. L. Sing, in: General Relativity Theory [Russian translation], Inostrannaya Literatura, Moscow (1963).Google Scholar
  11. 11.
    R. Tolmen, in: Relativity, Thermodynamics, and Cosmology [Russian translation], Nauka, Moscow (1974).Google Scholar
  12. 12.
    K. Meller, in: Relativity Theory [Russian translation], Atomizdat, Moscow (1975).Google Scholar
  13. 13.
    L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 6. Hydrodynamics [in Russian], Nauka, Moscow (1986).Google Scholar
  14. 14.
    C. Eckart, Phys. Rev., 58, No. 10, 919 (1940).zbMATHCrossRefADSGoogle Scholar
  15. 15.
    S. de Grot, V. Van Lewen, and H. Van Vert, Relativistic Kinetic Theory. Principles and Applications [Russian translation], Mir, Moscow (1983).Google Scholar
  16. 16.
    C. Cattaneo, Atti. Sem. Mat. Fis. Univ. Modena, 3, 3 (1948).Google Scholar
  17. 17.
    C. Cattaneo, Acad. Sci., 247, 431 (1958).Google Scholar
  18. 18.
    O. Yu. Dinariev, Dokl. Akad. Nauk SSSR, 301, No. 5, 1095 (1988).Google Scholar
  19. 19.
    O. Yu. Dinariev, Prikl. Mat. Mekh., 54, No. 1, 59 (1990).Google Scholar
  20. 20.
    O. Yu. Dinariev, Prikl. Mat. Mekh., 55, No. 6, 949 (1991).Google Scholar
  21. 21.
    O. Yu. Dinariev, Prikl. Mat. Mekh., 56, No. 2, 250 (1992).Google Scholar
  22. 22.
    O. Yu. Dinariev, Dokl. Ross. Akad. Nauk, 327, Nos. 4–6, 481 (1992).Google Scholar
  23. 23.
    O. Yu. Dinariev, Russ. Phys. J., No. 5, 456–430 (1992).Google Scholar
  24. 24.
    O. Yu. Dinariev, Prikl. Mat. Teor. Fiz., 42, No. 6, 47 (2001).zbMATHGoogle Scholar
  25. 25.
    O. Yu. Dinariev, Zh. Eksp. Teor. Fiz., 107, No. 6, 1877 (1995).Google Scholar
  26. 26.
    O. Yu. Dinariev, Zh. Eksp. Teor. Fiz., 110, No. 5, 1770 (1996).Google Scholar
  27. 27.
    O. Yu. Dinariev, Zh. Eksp. Teor. Fiz., 107, No. 5, 1573 (1995).Google Scholar
  28. 28.
    U. A. Day, in: Thermodynamics of Simple Media with Memory [Russian translation], Mir, Moscow (1974).Google Scholar
  29. 29.
    V. S. Vladimirov and A. G. Sergeev, in: Advances in Science and Engineering. Ser. Modern Problems in Mathematics. Fundamental Directions [in Russian], VINITI, Moscow (1985).Google Scholar
  30. 30.
    O. Yu. Dinariev, Dokl. Ross. Akad. Nauk, 309, No. 3, 615 (1989).Google Scholar
  31. 31.
    O. Yu. Dinariev, Dokl. Ross. Akad. Nauk, 319, No. 2, 356 (1991).ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.O. Yu. Schmidt Institute of Earth Physics of the Russian Academy of SciencesRussia

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