Anomalous Transport and Fractal Kinetics

  • G. M. Zaslavsky
Chapter
Part of the NATO ASI Series book series (NSSE, volume 218)

Abstract

An orbit of the passive particle transport is associated with a streamline of a flow, if the flow is inviscid, stationary and incompressible. In a general situation 3D flows have a nontrivial topology of streamlines due to their chaotic behaviour. As a result of the chaos the real space has a complicated structure of islands and stochastic sea of fractal or multifractal nature. Transport of a passive particle can be described as a random walk in a multifractal medium. It is important that the random walk is also fractal in time. Altogether, this produces nontrivial exponents of the asymptotic law of the average particle displacement. A kinetic equation of particle transport is described in many details to draw the attention to new nontrivial aspects of the statistical irreversibility. The multifractal transport creates the possibility of anomalous diffusion due to the Lévy process of a particle random walk or due to some analog of the Lévy process. Coherent structures in the random walk of a passive particle and its intermittency are features of the fractal or multifractal space-time nature.

Keywords

Random Walk Anomalous Diffusion Anomalous Transport Random Walk Process Passive Particle 
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. Afanas’ev, V.V., Sagdeev, R.Z., & Zaslavsky, G.M., 1991 Chaos, 1, 143.MathSciNetADSMATHCrossRefGoogle Scholar
  2. Chandrasek Star, S., 1943 Rev. Mod. Phys., 15, 1.ADSCrossRefGoogle Scholar
  3. Chernikov, A.A., Petrovichev, B.A., Rogalsky, A.V., Sagdeev, R.Z., & Zaslavsky, G.M., 1990 Phys. Lett. A, 144, 127.ADSCrossRefGoogle Scholar
  4. Douglas, J.F., 1989 Macromolucules 22, 1786.ADSCrossRefGoogle Scholar
  5. Gelfand, I.M. Si SHmov, G.E., 1958 Generalized Functions, vol. 1 (Moscow, Fizmat); translation 1964 ( Academic Press, New York. )Google Scholar
  6. Kolmogorov, A.N., 1938 Uspelchi Matem. Nauk., 5, 5.MathSciNetGoogle Scholar
  7. Ivy, P., 1937 Théorie de l’Addition des Variables Aléatoires ( Gauthier-Villars, Paris 1937 ).Google Scholar
  8. Lifshitz, E.M. & Pitaevsky, L.P., 1981 Physical Kinetics, ( Pergamon Press, Oxford. )Google Scholar
  9. Mandelbrot, B.B., 1982 The fractal nature of geometry, ( Freeman, San Francisco).MATHGoogle Scholar
  10. Montroll, E.W., & Shlesinger, M., 1984 In: Studies in statistical mechanics, v. 11, p. 1, Eds. J. Lebowitz and E.W. Montroll (North-Holland, Amsterdam ).Google Scholar
  11. Montroll, E.W., & Weiss, G.M., 1965 Journ. Math. Phys., 6, 167.MathSciNetADSCrossRefGoogle Scholar
  12. Petrovichev, B.A., Rogalsky, A.V., Sagdeev, R.Z., & Zaslavsky, G.M., 1990 Phys. Lett. A, 150, 391.MathSciNetADSCrossRefGoogle Scholar
  13. Ross, B., ed., 1975 Fractional Calculus and Its Applications, Lecture Notes 457 ( Springer-Verlag, New York ).MATHGoogle Scholar
  14. Shlesinger, M.F., 1989 Physica D, 38, 304.MathSciNetADSCrossRefGoogle Scholar
  15. Zaslavsky, G.M., 1991 Monte Verita Colloquium on Turbulence (to be published).Google Scholar
  16. Zaslavsky, G.M. & Tippett, M., 1991 Phys. Rev. Lett. 67, 3251.ADSCrossRefGoogle Scholar
  17. Zaslavsky, G.M., Sagdeev, R.Z. & Chernikov, A.A., 1988 Soy. Phys. -JETP, 67, 270.MathSciNetGoogle Scholar
  18. Zaslavsky, G.M., Zaicharov, M. Yu., Sagdeev, R.Z., Usncov, D.A., & Chernikov, A.A., 1986 Soy. Phys. -JETP 64, 294.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • G. M. Zaslavsky
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraUSA

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