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Asymptotic approach to the description of nonclassical transport processes. Fermat’s principle

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Abstract

A method has been proposed to calculate the concentration distribution at asymptotically long distances from a source of impurity in a medium including long-scale heterogeneities. It has been found that the exponent Γ ≫ 1 in an expression for the concentration satisfies a nonlinear equation with first-order partial derivatives. This has allowed using the variational principle to calculate the function Γ. The pre-exponential factor in the expression for the concentration has been determined in the leading approximation in the small parameter Γ−1. An analogy with geometrical optics and semiclassical approximation in quantum mechanics has been demonstrated.

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References

  1. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  2. M. B. Isichenko, Rev. Mod. Phys. 64, 961 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  3. D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge Univ. Press, Cambridge, 2000), p. 315.

    Book  MATH  Google Scholar 

  4. L. M. Zelenyi and A. V. Milovanov, Phys. Usp. 47, 749 (2004).

    Article  Google Scholar 

  5. I. L. Dranikov, P. S. Kondratenko, and L. V. Matveev, Dokl. Phys. 49, 22 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  6. I. L. Dranikov, P. S. Kondratenko, and L. V. Matveev, J. Exp. Theor. Phys. 98, 945 (2004).

    Article  ADS  Google Scholar 

  7. A. M. Dykhne, I. L. Dranikov, P. S. Kondratenko, and L. V. Matveev, Phys. Rev. E 72, 061104 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  8. A. M. Dykhne, P. S. Kondratenko, and L. V. Matveev, JETP Lett. 80, 410 (2004).

    Article  ADS  Google Scholar 

  9. L. Bolshov, P. Kondratenko, L. Matveev, and K. Pruess, Vadose Zone J. 26, 1152 (2008).

    Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).

    Google Scholar 

  11. Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media (Nauka, Moscow, 1980; Springer, Berlin, Heidelberg, 1990).

    Book  Google Scholar 

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, Moscow, 115191, Russia

    P. S. Kondratenko

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow region, 141700, Russia

    P. S. Kondratenko

Authors
  1. P. S. Kondratenko
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Correspondence to P. S. Kondratenko.

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Original Russian Text © P.S. Kondratenko, 2017, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 106, No. 9, pp. 581–584.

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Kondratenko, P.S. Asymptotic approach to the description of nonclassical transport processes. Fermat’s principle. Jetp Lett. 106, 604–607 (2017). https://doi.org/10.1134/S0021364017210068

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  • DOI: https://doi.org/10.1134/S0021364017210068

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