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Confined Anomalous Dynamics: A Fractional Diffusion Approach

Published online by Cambridge University Press:  10 February 2011

Ralf Metzler  and
Joseph Klafter
Ralf Metzler
Affiliation:
School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
Joseph Klafter
Affiliation:
School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
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Abstract

We study different boundary value problems for fractional diffusion equations which describe a non-Brownian particle. Absorbing and reflecting walls of a box, and the escape problem through a fluctuating bottleneck with coloured noise are considered.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 543: Symposium W – Dynamics in Small Confining Systems IV , 1998 , 281
Copyright
Copyright © Materials Research Society 1999

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References

[1] Bouchaud, J.-P. and Georges, A., Phys. Rep. 195, 12 (1990)Google Scholar
[2] Lévy, P., Calcul des probabilités (Gauthier–Villars Paris, 1925); Théorie de l'addition des variables aléatoires (Gauthier–Villars, Paris, 1937)Google Scholar
[3] Schneider, W. R. and Wyss, W., J. Math. Phys. 30, 134 (1989); R. Metzler, W. G. Glöckle and T. F. Nonnenmacher, Physica 211A, 13 (1994); R. Hilfer, Fractals 3, 211 (1995)Google Scholar
[4] Oldham, K. B. and Spanier, J., The fractional calculus (Academic Press, New York, 1974)Google Scholar
[5] Hilfer, R. and Anton, L., Phys. Rev. E 51, R848 (1995); A. Compte, Phys. Rev. E 53, 4191 (1996)Google Scholar
[6] West, B. J., Grigolini, P., Metzler, R. and Nonnenmacher, T. F., Phys. Rev. E 55, 99 (1997)Google Scholar
[7] Fogedby, H. C., Phys. Rev. E 58, 1690 (1998); Phys. Rev. Lett. 73, 2517 (1994); Phys. Rev. E 50, 1657 (1994)Google Scholar
[8] Metzler, R., Barkai, E. and Klafter, J. (submitted)Google Scholar
[9] Jespersen, S., Metzler, R. and Fogedby, H. C., Phys. Rev. E 59 (in press)Google Scholar
[10] Metzler, R., Barkai, E. and Klafter, J. (submitted) [Here, a derivation of fractional Fokker–Planck equations is given on the basis of a random walk model.]Google Scholar
[11] Feller, W., An Introduction to Probability Theory and its Applications (Wiley, New York, 1971), Vol. IIGoogle Scholar
[12] Compte, A., Metzler, R. and Camacho, J., Phys. Rev. E 56, 1445 (1997)Google Scholar
[13] Klafter, J., Blumen, A. and Shlesinger, M. F., Phys. Rev. A 35, 3081 (1987)Google Scholar
[14] Metzler, R., Klafter, J. and Sokolov, I., Phys. Rev. E 58, 1621 (1998)Google Scholar
[15] Metzler, R. and Klafter, J. (in preparation)Google Scholar
[16] Zwanzig, R., J. Stat. Phys. 97, 3587 (1992)Google Scholar
[17] Eizenberg, N. and Klafter, J., Chem. Phys. Lett. 243, 9 (1995), J. Stat. Phys. 104, 6796 (1996)Google Scholar
[18] Iben, I. E. T., Braunstein, D., Doster, W., Frauenfelder, H., Hong, M. K., Johnson, J. B., Luck, S., Ormos, P., Schulte, A., Steinbach, P. J., Xie, A. H. and Young, R. D., Phys. Rev. Lett. 62, 1916 (1989)Google Scholar
[19] Glöckle, W. G. and Nonnenmacher, T. F., Biophys. J. 68, 46 (1995)Google Scholar
[20] Wang, J. and Wolynes, P., Chem. Phys. Lett. 212, 427 (1993)Google Scholar
[21] Metzler, R., Klafter, J., Jortner, J. and Volk, M., Chem. Phys. Lett. 293, 477 (1998)Google Scholar
[22] Tables of Integral Transforms, edited by A., Erdélyi, Bateman Manuscript Project Vol. I (McGraw–Hill, New York, 1954)Google Scholar