Abstract
This second part reproduces a seminar (given by J.P. Bouchaud) which is intended to present the general mechanisms leading to anomalous diffusion laws. The central point of this analysis is that anomalous diffusion occurs when the Central Limit Theorem (C.L.T.) does not hold in its usual form. It is shown how simple arguments can be used to adapt the C.L.T. to these situations, thereby allowing to predict the resulting behaviors. Physical examples, which can be relevant to e.g. flows in porous media, are analysed accordingly.
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References
For a simple physical discussion, see J.P. Bouchaud, A. Georges, P. Le Doussal, J. Physique (Paris) 48 (1987) 1855.
See e.g. the courses by J. Brady and J. Koplik in this volume and also J.A. Aronovitz, D.R. Nelson, Phys. Rev. A 30 (1984) 1948, and references therein.
J. Villain, Phys. Rev. Lett. 52 (1984) 1543;
R. Maynard, J. Physique (Paris) Lettres 45 (1984) L81.
J. Bernasconi, H. Beyeler, S. Strässler, S. Alexander, Phys. Rev. Lett. 42 (1979) 819.
D. Amit, G. Parisi, L. Peliti, Phys. Rev. B 27 (1983) 1635.
F. Solomon, Ann. Probab. 3 (1975) 1;
H. Kesten, M. Kozlov and F. Spitzer, Compos. Math. 30 (1975) 145.
Ya. G. Sinaï in Lecture notes in Physics, Vol. 153, eds R. Sehrader, R. Seiler and D. Uhlenbrock, Springer, Berlin 1981.
B. Derrida, J. Stat. Phys. 31 (1983) 433;
B. Derrida and Y. Pomeau, Phys. Rev. Lett. 48 (1982) 627.
J.P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal, Europhysics Lett. 3 (1987) 653.
E. Marinari, G. Parisi, D. Ruelle, P. Windey, Phys. Rev. Lett. 50 (1983) 1223,
E. Marinari, G. Parisi, D. Ruelle, P. Windey, Commun. Math. Phys. 89 (1983) 1.
The d-dimensional case with short range correlations has been studied in: J.M. Luck Nuel Phys. B 225 (1983) 169
D.S. Fisher, Phys. Rev. A 30 (1984) 960
V.E. Kravtsov, I.V. Kerner and V.I. Yudson, J. Phys. A Math. Gen. 18 (1985) L703.
The full analysis including long-range correlations has been performed by J.P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal, J. Physique (Paris) 48 (1987) 1445.
J. Brady and D. Koch, this volume.
G. de Marsily and G. Matheron, Water Resources Research 16 (1980) 901.
See the chapter by J.P. Hulin and D. Salin, this volume.
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© 1988 Kluwer Academic Publishers
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Bouchaud, J.P., Georges, A. (1988). The Physical Mechanisms of Anomalous Diffusion. In: Guyon, E., Nadal, JP., Pomeau, Y. (eds) Disorder and Mixing. NATO ASI Series, vol 152. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2825-1_2
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DOI: https://doi.org/10.1007/978-94-009-2825-1_2
Publisher Name: Springer, Dordrecht
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