EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 11 / No 3 (2016) Math. Model. Nat. Phenom., 11 3 (2016) 107-127 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
Page(s) 107 - 127
DOI https://doi.org/10.1051/mmnp/201611307
Published online 21 June 2016
  1. M. Abel, A. Celani, D. Vergni and A. Vulpiani, Front propagation in laminar flows, Phys. Rev. E, 64 (2001), 046307. [CrossRef] [Google Scholar]
  2. E. Agliari, Exact mean first-passage time on the T-graph, Phys. Rev. E, 77 (2008), 011128. [CrossRef] [Google Scholar]
  3. S. Alexander, R. Orbach. Density of states on fractals: fractons. J. Phys. Lett., 43 (1982), 625–631. [Google Scholar]
  4. K. Andersen, P. Castiglione, A. Mazzino, A. Vulpiani. Simple stochastic models showing strong anomalous diffusion. Eur. Phys. J., B 18 (2000), 447–452. [CrossRef] [EDP Sciences] [Google Scholar]
  5. M. Avellaneda and A.J. Majda. An integral-representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows. Commun. Math. Phys., 138 (1991), 339–391. [CrossRef] [Google Scholar]
  6. M. Avellaneda and M. Vergassola. Stieltjes integral representation of effective diffusivities in time-dependent flows. Phys. Rev. E, 52 (1995), 3249–3251. [CrossRef] [MathSciNet] [Google Scholar]
  7. D. Bertacchi. Asymptotic behaviour of the simple random walk on the 2-dimensional comb. Electron. J. Probab, 11 (2006) 1184-1203. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Boffetta, A. Celani, A. Crisanti, A. Vulpiani. Pair dispersion in synthetic fully developed turbulence. Phys. Rev. E, 60 (1999) 6734–6741. [CrossRef] [Google Scholar]
  9. G. Boffetta, I. M. Sokolov. Statistics of two-particle dispersion in two-dimensional turbulence. Phys. Fluids 14 (2002), 3224–3232. [CrossRef] [Google Scholar]
  10. B. Bollobás. Modern Graph theory. Springer-Verlag, New York, 1998. [Google Scholar]
  11. J.P. Bouchaud, A. Georges. Anomalous diffusion in disordered media. Phys. Rep., 195 (1990), 127–293. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Burioni, D. Cassi. Fractals without anomalous diffusion. Phys. Rev. E, 49 (1994), R1785–R1787. [CrossRef] [Google Scholar]
  13. R. Burioni, D. Cassi. Spectral dimension of fractal trees. Phys. Rev. E, 51 (1995), 2865–2869. [CrossRef] [Google Scholar]
  14. R. Burioni, S. Chibbaro, D. Vergni, A. Vulpiani, Reaction spreading on graphs. Phys. Rev. E, 86 (2012), 055101–055104. [CrossRef] [Google Scholar]
  15. D. Cassi, R. Sofia. Random walks on d-dimensional comb Lattices. Mod. Phys. Lett., B 6 (1992), 1397–1403. [CrossRef] [Google Scholar]
  16. P. Castiglione, A. Mazzino, P. Muratore-Ginanneschi, A. Vulpiani. On strong anomalous diffusion. Physica D, 134 (1999), 75–93. [NASA ADS] [CrossRef] [Google Scholar]
  17. J.W. Chamberlain, D.M. Hunten. Theory of Planetary Atmospheres: An Introduction to Their Physics and Chemistry. Academic Press, New York 1987. [Google Scholar]
  18. W.J. Cocke. Turbulent Hydrodynamic Line Stretching: Consequences of Isotropy. Phys. Fluids, 12 (1969), 2488–2492. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.E. Fisher. Shape of a Self-Avoiding Walk or Polymer Chain. J. Chem. Phys., 44 (1966), 616–622. [CrossRef] [Google Scholar]
  20. R.A. Fisher. The wave of advance of advantageous genes. Ann. Hum. Genet., 7 (1937), 355–369. [Google Scholar]
  21. G. Forte, R. Burioni, F. Cecconi and A. Vulpiani, Anomalous diffusion and response in branched systems: a simple analysis. J. Phys.: Condens. Matter, 25 (2013), 465106. [CrossRef] [Google Scholar]
  22. G. Forte, F. Cecconi and A. Vulpiani. Non-anomalous diffusion is not always Gaussian. Eur. Phys. J. B, 87 (2014), 102–111. [CrossRef] [Google Scholar]
  23. M. Freidlin. Functional integration and partial differential equations. Princeton University Press, Princeton NJ, 1985. [Google Scholar]
  24. U. Frisch. Turbulence. The legacy of A.N. Kolmogorov. Cambridge University Press, Cambridge (UK) 1995. [Google Scholar]
  25. A. Gabrielli, F. Cecconi. Diffusion, super-diffusion and coalescence from single step. J. Stat. Mech. (2007), P10007. [Google Scholar]
  26. B. Gnedenko and A.N. Kolmogorov. Limit distribution for Sums of Independent Random Variables. Addison-Wesley, 1954. [Google Scholar]
  27. R. Ishizaki, T. Horita, T. Kobayashi, H. Mori. Anomalous diffusion due to accelerator modes in the standard map. Prog. Theor. Phys., 85 (1991), 1013–1022. [CrossRef] [Google Scholar]
  28. J. Klafter and I.M. Sokolov. First steps in random walks: from tools to applications. Oxford University Press, New York, 2011. [Google Scholar]
  29. R. Klages. G. Radons. I.M. Sokolov. Anomalous transport: foundations and applications. Wiley-VCH Verlag GmbH & Co. Weinheim (DE) (2008). [Google Scholar]
  30. X.P. Kong and E.G.D. Cohen. Anomalous diffusion in a lattice-gas wind-tree model. Phys. Rev. B, 40 (1989), 4838-4845. [CrossRef] [Google Scholar]
  31. J. Klafter, M. F. Shlesinger, G. Zumofen. Beyond brownian motion. Physics Today, 49 (1996), 33–39. [Google Scholar]
  32. A.N. Kolmogorov, I.G. Petrovskii, N.S. Piskunov, A study of the diffusion equation with increase in the quantity of matter, and its application to a biological problem. Bull. Moscow Univ. Math., A 1 (1937), 1–25. [Google Scholar]
  33. A.J. Lichtenberg, M.A. Lieberman. Regular and Chaotic Dynamics. Springer-Verlag, New York, 1991. [Google Scholar]
  34. A.J. Majda, P.R. Kramer. Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena. Phys. Rep., 314 (1999), 237–574. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  35. R. Mancinelli, D. Vergni and A. Vulpiani. Superfast front propagation in reactive systems with anomalous diffusion. Eur. Phys. Lett., (2002) 60, 532–538. [CrossRef] [EDP Sciences] [Google Scholar]
  36. R. Mancinelli, D. Vergni and A. Vulpiani. Front propagation in reactive systems with anomalous diffusion. Physica D, 85 (2003), 175–195. [CrossRef] [Google Scholar]
  37. B. Mandelbrot. The Fractal Geometry of Nature. Freeman, San Francisco, 1983. [Google Scholar]
  38. T. Manos and M. Robnik. Survey on the role of accelerator modes for anomalous diffusion: The case of the standard map. Phys. Rev. E, 89 (2014), 022905. [CrossRef] [Google Scholar]
  39. R.N. Mantegna, H.E. Stanley. Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. Phys. Rev. Lett., 73 (1994), 2946–2949. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  40. G. Matheron, G. De Marsily. Is transport in porous media always diffusive?. Water Resources Res., 16 (1980), 901–917. [CrossRef] [Google Scholar]
  41. V. Méndez, A. Iomin, D. Campos and W. Horsthemke. Mesoscopic description of random walks on combs. Phys. Rev. E, 92 (2015), 062112. [CrossRef] [Google Scholar]
  42. J.D. Murray. Mathematical Biology, Springer, Berlin 1993. [Google Scholar]
  43. Z. Neufeld and E. Hernández-García. Chemical and Biological Processes in Fluid Flows: A Dynamical Systems Approach. World Scientific, Singapore 2009. [Google Scholar]
  44. B. O’Shaughnessy, I. Procaccia. Diffusion on fractals. Phys. Rev. A, 32 (1985), 3073–3083; [Google Scholar]
  45. A. Okubo, S.A. Levin. Diffusion and Ecological Problems: Modern Perspectives, Science & Business Media vol. 14, Springer, Berlin 2013. [Google Scholar]
  46. H.R. Pruppacher, J.D. Klett. Microphysics of clouds and precipitation. Kluwer Academic Plubisher, Boston 1998. [Google Scholar]
  47. A.B. Rechester, R.B. White. Calculation of turbulent diffusion for the Chirikov-Taylor model. Phys. Rev. Lett., 44 (1980), 1586–1589. [CrossRef] [Google Scholar]
  48. L.F. Richardson. Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond., A 110 (1926), 709–737. [Google Scholar]
  49. D.E. Rosner. Transport processes in chemically reacting flow systems. Butterworth-Heinemann, Boston 2013. [Google Scholar]
  50. M.F. Schlesinger, B. West, J. Klafter. Lévy dynamics of enhanced diffusion: Application to turbulence. Phys. Rev. Lett., 58 (1987), 1100–1104. [NASA ADS] [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  51. N.G. Van Kampen. Stochastic processes in physics and chemistry. Elsevier, 1992. [Google Scholar]
  52. V.A. Volpert, Y. Nec, A.A. Nepomnyashchy, Exact solutions in front propagation problems with superdiffusion. Physica D, 239 (2010), 134–144. [CrossRef] [Google Scholar]
  53. J.B. Weiss, A. Provenzale, eds. Transport and mixing in geophysical flows. vol. 744. Springer, Berlin 2007. [Google Scholar]
  54. G.M. Zaslavsky, D. Stevens, A. Weitzener. Self-similar transport in incomplete chaos. Phys. Rev. E, 48 (1993), 1683–1694. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.