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Homogenization and Renormalization of Multiple-Scattering Expansions for Green Functions in Turbulent Transport

  • Marco Avellaneda
  • Andrew J. Majda
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)

Abstract

The purpose of this article is to report on a method for averaging equations with rapidly varying characteristics, based on the asymptotic analysis of the perturbation expansions for the corresponding Green functions. While such methodology is relevant to many problems in homogenization, we shall discuss it primarily in the context of advection-diffusion equations describing passive turbulence transport.

Keywords

Green Function Perturbation Parameter Turbulent Transport Fourier Multiplier Simple Shear Flow 
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References

  1. 1.
    M. Lax, Rev. Mod. Phys. 23, 287 (1951).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    M. Bixon and R. Zwanzig, J. Chem. Phys. 75, 2354 (1981).CrossRefGoogle Scholar
  3. 3.
    T.R. Kirkpatrick, J. Chem. Phys. 76, 4255 (1982).CrossRefGoogle Scholar
  4. 4.
    G.H. Fredrickson and E.S.G. Shaqfeh, Phys. Fluids AVol.1, 1, January 1989.CrossRefGoogle Scholar
  5. 5.
    M. Beran, Statistical Continuum Theories, Wiley-Interscience, New York (1968).MATHGoogle Scholar
  6. 6.
    J.R. Willis, in Advances in Applied Mechanics, 21, p. 1–78, C-S. Yih, Ed. Academic Press, New York, 1981.CrossRefGoogle Scholar
  7. 7.
    D.G. Bergman, Phys. Rep. Phys. Lett. C., 43, 377 (1978).MathSciNetGoogle Scholar
  8. 8.
    G.W. Milton, J. Appl. Phys. 42, 5286 (1982).Google Scholar
  9. 9.
    K. Golden and G.C. Papanicolaou, Comm. Math. Phys. 90, 470 (1983).MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Avellaneda and A.J. Majda, Phys. Rev. Lett. 62, 753 (1989).CrossRefGoogle Scholar
  11. 11.
    M. Avellaneda and A.J. Majda, preprint, submitted to Physica D, January 1990.Google Scholar
  12. 12.
    P.G. Wolynes, Phys. Rev. A11, 1700 (1975).CrossRefGoogle Scholar
  13. 13.
    see articles in ThePadé Approximant in Theoretical Physics, G.A. Baker, Jr., and J.L. Gammel, eds., Academic Press, New York, 1970.Google Scholar
  14. 14.
    R. Kraichnan, in Ref. 13CrossRefGoogle Scholar
  15. 15.
    L. Tartar, in Essays of Mathematical Analysis in Honour of E. de Giorgi, Birkhauser, 1989.Google Scholar
  16. 16.
    Y. Amirat, K. Hamdache and A. Ziani, Ann. Inst. Henri Poincaré, Anal. non linéaire 6(5), 397 (1989).MathSciNetMATHGoogle Scholar
  17. 17.
    Y. Amirat, K. Hamdache and A. Ziani, preprint, January 1990.Google Scholar
  18. 18.
    G. Mathéron and G. de Marsily, Water Resources Reseasrch, 16(5), 901 (1980).CrossRefGoogle Scholar
  19. 19.
    J.P. Bouchaud, A. Comptet, A. Georges, P. Le Doussal, Journ. Phys. (Paris) 48, 1445 (1987).CrossRefGoogle Scholar
  20. 20.
    D.L. Koch and J.F. Brady, Phys. Fluids A, 1, 47 (1989).MATHCrossRefGoogle Scholar
  21. 21.
    M. Avellaneda and A. Majda, preprint, Dec. 1989, to appear in Comm. Math. Phys.Google Scholar
  22. 22.
    K. Oelschläger, Annals of Prob. 16(3), 1084 (1988).MATHCrossRefGoogle Scholar
  23. 23.
    G.C. Papanicolaou and S.R.S. Varadhan, in Random Fields, Coll. Math. Soc. Janos Bolyai, (J. Fritz, J.L. Leibowitz, D. Szasz, eds.), p. 835–873, North-Holland, Amsterdam (1982).Google Scholar
  24. 24.
    I.M. Gelfand and Vilenkin H, Generalized Fuctions, Vol.IV, Academic Press, New York, London, 1964.Google Scholar
  25. 25.
    N.I. Ahiezer and M. Krein, Some Questions in the Theory of Moments, Trans. of Math. Monographs, 2, American Mathematical Society, Rhode Island, 1962.Google Scholar
  26. 26.
    S.G. Mihlin, Dok. Akad. Nauk.109, 701 (1956).MathSciNetGoogle Scholar
  27. 27.
    M. Avellaneda and A. Majda, in preparation.Google Scholar
  28. 28.
    S.M. Kozlov, Russian Math. Surv. 40(2), 73 (1985).Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Marco Avellaneda
    • 1
  • Andrew J. Majda
    • 2
  1. 1.Courant InstituteNew York UniversityNew YorkUSA
  2. 2.Program for Computational and Applied Mathematics Department of MathematicsPrinceton UniversityPrincetonUSA

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