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Journal of Statistical Physics

, Volume 12, Issue 4, pp 311–359 | Cite as

Nonanalytic dispersion relations for classical fluids

II. The general fluid
  • M. H. Ernst
  • J. R. Dorfman
Articles

Abstract

The analytic structure of the hydrodynamic frequenciesz(k) for the sound, heat, and shear modes and of the hydrodynamic equations for a monatomic fluid are discussed on the basis of the mode-mode coupling theory. It is shown that the hydrodynamic frequencies depend on the wave numberk, for smallk, asz(k) = ak + bk2 +\(z(k) = ak + bk^2 + \sum\nolimits_{n = 1}^\infty {c_n k^{3 - 2^{ - n} } } \) and that some of the correlation functions that appear in the Fourier-Laplace transforms of the hydrodynamic equations contain branch point singularities. The implications of these results for the derivation of linear hydrodynamic equations, such as the Burnett equations, and for the long-time behavior of time correlation functions are discussed.

Key words

Statistical mechanics nonequilibrium statistical mechanics hydrodynamic equations Navier-Stokes equations Burnett equations time correlation functions 

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References

  1. 1.
    M. H. Ernst and J. R. Dorfman,Physica 61:157 (1972).Google Scholar
  2. 2.
    L. P. Kadanoff and J. Swift,Phys. Rev. 166:89 (1968).Google Scholar
  3. 3.
    K. Kawasaki,Ann. Physics 61:1 (1970); see also M. S. Green, ed.,Critical Phenomena Academic Press, New York (1971), p. 342Google Scholar
  4. 4.
    R. A. Ferrell,Phys. Rev. Letters 24:1169 (1970); and inDynamical Aspects of Critical Phenomena, J. I. Budnick and M. P. Kawatra, eds., Gordon & Breach, New York (1972), p. 1.Google Scholar
  5. 5.
    M. H. Ernst, E. H. Hauge, and J. M. J. Van Leeuwen,Phys. Rev. Letters 25:1254 (1970);Phys. Rev. A 4:2055 (1971);Phys. Letters 34A:419 (1971); and to be published; see also J. R. Dorfman, inThe Boltzmann Equation, E. G. D. Cohen and W. Thirring, eds., Springer-Verlag, Wein (1973), p. 209.Google Scholar
  6. 6.
    Y. Pomeau,Phys. Rev. A 5:2569 (1972);7:1134 (1973);Phys. Lett. 38A:245 (1972).Google Scholar
  7. 7.
    J. Dufty,Phys. Rev. A 5:2247 (1972).Google Scholar
  8. 8.
    R. Zwanzig, inLectures in Theoretical Physics, III, W. E. Brittin, B. W. Downs, and J. Downs, eds., Interscience, New York (1961), p. 106.Google Scholar
  9. 9.
    P. Schofield, inPhysics of Simple Liquids, H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbrooke, eds., North-Holland, Amsterdam (1968), p. 563.Google Scholar
  10. 10.
    J. M. J. Van Leeuwen and M. H. Ernst, unpublished report.Google Scholar
  11. 11.
    M. H. Ernst and J. R. Dorfman,Phys. Letters 38A:269 (1972).Google Scholar
  12. 12.
    M. H. Ernst, E. H. Hauge, and J. M. J. Van Leeuwen, to be published.Google Scholar
  13. 13.
    I. de Schepper and M. H. Ernst, to be published.Google Scholar
  14. 14.
    C. S. Wang Chang and G. E. Uhlenbeck, inStudies in Statistical Mechanics, Vol. V, J. de Boer and G. E. Uhlenbeck, eds., North-Holland, Amsterdam (1970), p. 1.Google Scholar
  15. 15.
    S. Chapman and T. G. Cowling,Mathematical Theory of Non-Uniform Gases, 3rd ed., Cambridge Univ. Press (1970).Google Scholar
  16. 16.
    T. Keyes and I. Oppenheim,Physica 70:100 (1973).Google Scholar
  17. 17.
    J. Dufty and J. A. McLennan,Phys. Rev. A 9:1266 (1974).Google Scholar
  18. 18.
    I. de Schepper, H. van Beijeren, and M. H. Ernst,Physica 75:1 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • M. H. Ernst
    • 1
  • J. R. Dorfman
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtThe Netherlands
  2. 2.Institute for Fluid Dynamics and Applied Mathematics, and Department of Physics and AstronomyUniversity of MarylandMaryland

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