Advertisement

The European Physical Journal Special Topics

, Volume 143, Issue 1, pp 209–215 | Cite as

Generalized diffusion and pretransitional fluctuations statistics

  • J.-P. Boon
  • P. Grosfils
  • J. F. Lutsko
Article
  • 46 Downloads

Abstract.

(a) For diffusion type processes, non-Gaussian distributions are obtained, in a generic manner, from a generalization of classical linear response theory; (b) Statistical properties of hydrodynamic fields reveal pretransitional fluctuations in fingering processes, and these precursors are found to exhibit power law distributions; (c) These power laws are shown to follow from q-Gaussian structures which are solutions to the generalized diffusion equation. The present analysis (i) offers a physical picture of the precursors dynamics, (ii) suggests a physical interpretation of nonextensivity from the structure of the precursors, and (iii) provides an illustration of the emergence of statistics from dynamics.

Keywords

Vorticity European Physical Journal Special Topic Porous Media Equation Classical Statistical Mechanic Lattice Boltzmann Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Muskat, The Flow of Homogeneous Fluids through Porous Media (McGraw-Hill, New York, 1937) Google Scholar
  2. A.R. Plastino, A. Plastino, Physica A 222, 347 (1995) CrossRefADSMathSciNetGoogle Scholar
  3. C. Tsallis, D.J. Bukman, Phys. Rev. E 54, R2197 (1996) Google Scholar
  4. J.F. Lutsko, J.P. Boon, Europhys. Lett. 71, 906 (2005) CrossRefADSGoogle Scholar
  5. P. Grosfils, J.P. Boon, Europhys. Lett. 74, 609 (2006) CrossRefADSGoogle Scholar
  6. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 1981) Google Scholar
  7. G.M. Homsy, Ann. Rev. Fluid Mech. 19, 271 (1987) CrossRefADSGoogle Scholar
  8. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics (Clarendon Press, Oxford, 2001) Google Scholar
  9. C. Beck, G.S. Lewis, H.L. Swinney, Phys. Rev. E 63, 035303(R) (2001) CrossRefADSGoogle Scholar
  10. P. Grosfils, J.P. Boon, J. Chin, E.S. Boek, Phil. Trans. Royal Soc. 362, 1723 (2004) CrossRefADSMathSciNetGoogle Scholar
  11. G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasi-Regular Patterns (Cambridge University Press, Cambridge, 1991); Sect. 7.4 Google Scholar
  12. See e.g. EuroPhysics News 36/6, 183-231 (2005) Google Scholar
  13. A. De Wit, G.M. Homsy, J. Chem. Phys. 110, 8663 (1999); see Fig. 6 and Sect. V.B CrossRefADSGoogle Scholar
  14. E.G.D. Cohen, Physics A 305, 19 (2002) zbMATHCrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • J.-P. Boon
    • 1
  • P. Grosfils
    • 2
  • J. F. Lutsko
    • 1
  1. 1.Physics Department, CP 231Université Libre de BruxellesBruxellesBelgium
  2. 2.Chimie Physique, E.P. CP 165/62, Université Libre de BruxellesBruxellesBelgium

Personalised recommendations