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Licensed Unlicensed Requires Authentication Published by De Gruyter June 11, 2013

Beyond fick's equations, an overview

Jean Philibert


Fick's equations do not allow modelling of a large number of diffusion phenomena. Several extensions are described and some applications outside the field of physical metallurgy are briefly described. Departure from Brownian motion appears to be very common, so that anomalous diffusion would actually appear as normal.

* Correspondence address, Prof. Jean Philibert 24 rue Sainte Radegonde F-78100 Saint-Germain-en-Laye, France Tel.: +33 1 39 73 29 37 E-mail:


[1] J.Philibert, in: J.Kärger, F.Grinberg, P.Heitjans (Eds.), Diffusion Fundamentals, LeipzigUniversitätsverlag (2005) 817.Search in Google Scholar

[2] see for example: J. Philibert, Atom Movements, Diffusion and Mass Transport in solids, Les Editions de Physique (1991) or H. Mehrer, Diffusion in Solids, Fundamentals, Methods, Materials, Diffusion controlled Processes, Springer-Verlag (2007).Search in Google Scholar

[3] D.L. Beke, I.A. Szabo (Eds.): Diffusion and Stresses, Scitec #Publ., Def. Diff. Forum 129–130 (1996). D.L. Beke, Z. Erdeliy, #I.A. Szabo (Eds.), Diffusion and Stresses, Trans. Tech. Publ., Def. Diff. Forum 264 (2007).Search in Google Scholar

[4] G.Martin: Phys. Rev. B 30, 1424 (1984).10.1103/PhysRevB.30.1424Search in Google Scholar

[5] A.J.Ammermann, L.L.Cavalli-Sforza: Neolithic Transition and the Genetics of Population in Europe, Princeton University Press (1984).10.1525/aa.1987.89.2.02a00190Search in Google Scholar

[6] G.Vogl: Wandern ohne Ziel. Von der Atomdiffusion zur Ausbreitung von Lebenwesen und Idee, Springer-Verlag, Berlin Heidelberg (2007).Search in Google Scholar

[7] B.Wen: Nature431 (2004) 302.10.1111/j.1740-0929.2009.00689.xSearch in Google Scholar

[8] D.Le Bihan, S.Urayama, T.Aso, T.Hanakawa, H.Fukuyama: Proc. Natl. Acad. Sci. USA103 (2006) 82638.10.1073/pnas.0600644103Search in Google Scholar

[9] D.Le Bihan: La Recherche N°410 (2007) 4649.Search in Google Scholar

[10] J.P.Bouchaud, A.Georges: Phys. Rep.195 (1990) 127293.10.1016/0370-1573(90)90099-NSearch in Google Scholar

[11] J.Klafter, I.M.Sokolov: Physics World18 (2005) 2932.10.1088/2058-7058/18/8/33Search in Google Scholar

[12] PaulLévy: Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris (1954).Search in Google Scholar

[13] M.Gilbert, S.Guichard, J.Freise, J,-C.Grégoire, W.Heitland, N.Straw, C.Tilbury, S.Augustin: J. Appl. Ecology42 (2005) 805813.10.1111/j.1365-2664.2005.01074.xSearch in Google Scholar

[14] I.M.Sokolov, J.Klafter, A.Blumen: Physics Today (Nov. 2002) 48–54.10.1063/1.1535007Search in Google Scholar

[15] H.Scher, E.Montroll: Phys. Rev. B12 (1975) 24552477.10.1103/PhysRevB.12.2455Search in Google Scholar

[16] O.Cardoso, P.Tabeling: Europhys. Letters7 (1988) 255.Search in Google Scholar

[17] T.Kosztolowicz, in: J.Kärger, F.Grinberg, P.Heitjans (Eds.), Diffusion Fundamentals, LeipzigUniversitätsverlag (2005) 572573.Search in Google Scholar

[18] A.Ott, J.P.Bouchaud, D.Langevin, W.Urbach: Phys. Rev. Letters65 (1990) 2201.Search in Google Scholar

[19] R.Weeks, T.H.Solomon, J.S.Urbach, H.L.Swinney, in:, M.F.Shlesinger, G.M.Zaslavsky, U.Frisch (Eds.), Lévy flights and related topics in physics, Springer-Verlag (1995) 5171.10.1007/3-540-59222-9_25Search in Google Scholar

[20] D.Brockmann, L.Hufnagel, T.Geisel: Nature439 (2006) 462465.10.1007/978-3-642-17776-7_68Search in Google Scholar

[21] L.F.Richardson: Proc. Roy. Soc. London, A 110, (1926) 709.10.1098/rspa.1926.0043Search in Google Scholar

[22] P.Bellon, R.S.Averback, S.Odunuga, Y.Li, P.Krasnochtchekov: Phys. Rev. Letters99 (2007) 110602.Search in Google Scholar

Received: 2009-2-11
Accepted: 2009-4-8
Published Online: 2013-06-11
Published in Print: 2009-06-01

© 2009, Carl Hanser Verlag, München

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