Abstract
We recall the main features of the fluctuations of self similar interfaces which can be observed in diffusion, invasion of a porous medium by a fluid, thin magnetic films of even corrosion patterns. The relations of this behavior with other physical problems like fragmentation of clusters, cluster dynamics of a lattice gas of particles, or some features of dynamical percolation is also presented. Finally its connections with interface depinning and growth of rough surfaces is discussed.
Preview
Unable to display preview. Download preview PDF.
References
A. H. Thompson, A. J. Katz and R. Raschke, Phys. Rev. Lett. 59 (1987) 29; J. P. Stokes, A. P. Kushnick and M. O. Robbins, Phys. Rev. Lett. 60 (1988) 1386; K. J. Maløy, L. Furuberg, J. Feder and T. Jøssang, Phys. Rev. Lett. 68 (1992) 2161
Y. Imry and S. Ma, Phys. Rev. Lett. 35 (1975) 1399; G. J. Grinstein, J. Appl. Phys. 55 (1984) 2371; A. Kirilyuk, J. Ferré and D. Renard, Europhys. Lett. 24 (1993) 403
J. L. Hudson, J. Tabora, K. Krisher and I. G. Krevrekidis, Phys. Lett. A. 179 (1993) 355; D. E. Williams, R. C. Newman, Q. Song and R. G. Kelly, Nature (London) 350 (1991) 216; L. Balázs, L. Nyikos, 1. Szabó, and R. Schiller, preprint.
See “Charge Density Waves in Solids”, edited by G. Hutiray and J. Solyom, Lecture Notes in Physics, vol. 217 (Springer Verlag, Berlin, 1985).
B. Sapoval, M. Rosso, J. F. Gouyet and J. F. Colonna, Solid State Ionics 18 & 19 (1986) 21.
D. Sornette, Phys. Rev. Lett. 69 (1992) 1287; T. L. Chelidze, Phys. Earth. Planet. Inter. 28 (1982) 93; G. A. Sobolev, Pure Appl. Geophys. 124 (1986) 811.
G. Mackay and N. Jan, J. Phys. A17 (1984) L
D. Dhar, Phys. Rev. Lett. 64 (1990) 1613.
L. Furuberg, J. Feder, A. Aharony and T. Jøssang, Phys. Rev. Lett. 61 (1988) 2117.
A. H. Thompson, A. J. Katz and C. E. Krohn, Advances in Physics, 36 (1987) 625.
P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59 (1981) 381.
B. Sapoval, M. Rosso and J. F. Gouyet, J. Phys. (Paris) Lett. 46 (1985) L149.
L. H. Tang and H. Leschhorn, Phys. Rev. 45 (1992) R8309.
S. V. Buldyrev, A. L. Barabäsi, F. Caserta, S. Havlin, H. E. Stanley and T. Vicsek, Phys. Rev. A 45 (1992) R8313; L. A. N. Amaral, A. L. Barabäsi, S. V. Buldyrev, S. Havlin and H. E. Stanley, Fractals 1 (1993) 818, the rupture lines in paper sheets, seem to have a very similar behavior, see J. Kertész, V. K Horváth and F. Weber, Fractals, 1 (1993) 67.
J. F. Gouyet and Y. Boughaleb, Phys. Rev. B40 (1989) 4760; B. Sapoval, Philos. Mag. B 59 (1989) 75.
J. F. Gouyet, B. Sapoval, Y. Boughaleb and M. Rosso, Physica A 157 (1989) 620.
S. Roux and E. Guyon, J. Phys. A 22. (1989) 3693.
J. F. Gouyet, Physica A 168 (1990) 581.
N. Martys, M. O. Robbins and M. Cieplak, Phys. Rev. B 44 (1991) 12294.
V. A. Mukhamedov, private communication.
H. J. Hermann, J. Phys. A26 (1993) L1145; W. R. Roseen and C. K. Mamun, Phys. Rev. B 47 (1993) 11815; S. M. Clifford, J. Geophys. Res. E 98 (1993) 10973; P. Meakin, A. Birovljev, V. Frette, J. Feder and T. Jøssang, Physica A 191 (1992) 227; J. J. E. Herrera, Physica D 57 (1992) 249; L. Furuberg, A. Hansen, E. Hinrichsen, J. Feder and T. Jøssang, Phys. Scr. 38(1991) 91; R. Pandey and S. Yu, J. Phys. A 24 (1991) 3959; S. Roux and E. Guyon, J. Phys. A 24 (1991) 1611.
J. F. Gouyet, in “Soft Order in Physical Systems”, R. Bruisma and Y. Rabin eds., Plenum Pub. Corp., New York, 1993.
J. F. Gouyet, Phys. Rev. B 47 (1993) 5446.
S. D. Druger, A. Nitzanand M. A. Ratner,J.Chem.Phys. 76 (1983) 3133; A. K. Harrison and R. Zwanzig, Phys. Rev. A 32 (1985) 1072.
T. Grossman and A. Aharony, J. Phys. A 20 (1986) L745.
M. Rosso, J. F. Gouyet and B. Sapoval, Phys. Rev. Lett. 57 (1986) 3195; J. F. Gouyet, M. Rosso and B. Sapoval, Phys. Rev. B 37 (1988) 1832.
jΔpjαN is the surface of the front. It can also be written as a function of the width (σft)D f-d+1 and corresponds, as a function of concentration to (xc is such that p(ξc) = pc) | p(ξc ± Oft)-p(ξc)| −v(Df-d+1) whose exponent is the exponent w of ref. [19]. The exponent ψs was also found from very different arguments by Martys et al. [19] (and called r′)
J. F. Gouyet, April 1991, unpublished.
A. R. Kerstein, J. Phys. A 22 (1989) 3371.
M. F Gyure and B. F. Edwards, Phys. Rev. Lett. 68 (1992) 2692; B. F. Edwards, M. F. Gyure and M. Ferer, Phys. Rev. A 46 (1992) 6252.
W. Kintzel, in Percolation Structures and Processes, G. Deutcher, R. Zallen and J. Adler eds., Annals of the Israel Physical Society, 1983, vol. 5, chap.. 18.
T. Vicsek, Fractal Growth Phenomena, 2nd ed., part IV (World Scientific Singapore, 1992); J. F. Gouyet, M. Rosso and B. Sapoval, in Fractals and Disordered Systems, A. Bundle and S. Havlin eds. (Springer Verlag, Heidelberg, 1992); Dynamics of Fractal Surfaces, F. Family and T. Vicsek eds. (World Scientific Singapore, 1991); Les Houches Workshop, R. Jullien, J. Kertesz, P. Meakin and D. E. Wolf eds.(Nova Science, New York, 1992), P. Meakin, Phys. Rep. (to appear); T. HalpinHealey and Y. C. Zhang, Phys. Rev. (to appear).
J. P. Nadal, R. M. Bradley and P. N. Strenski, J. Phys. A 19 (1986) L505.
M. Cieplak and M. O. Robbins, Phys. Rev. Lett. 60 (1988)2042.
M. Martys, M. Cieplak and M. O. Robbins, Phys. Rev. Lett. 66 (1991) 1058.
C. S. Nolle, B. Koiller, M. Martys and M. O. Robbins, preprint.
H. Ji and M. O. Robbins, Phys. Rev. B 46 (1992) 14519.
V. K. Horvath, F. Family and T. Vicsek, J. Phys. A 24 (1991) L25.
M. A. Rubio, C. A. Edwards, A. Dougherty and J. P. Gollub, Phys. Rev. Lett. 63 (1989) 1685.
S. He, G. Kahanda and P. Z. Wong, Phys. Rev. Lett. 69 (1992) 3731.
S. V. Buldyrev, A. L. Barabäsi, S. Havlin, J. Kertesz, H. E. Stanley and H. Xenias, Physica A 191 (1992) 220.
K. Sneppen, Phys. Rev. Lett. 69 (1992) 3539; see also Z. Olami, I. Procaccia and R. Zeitak, Phys. Rev. E 49 (1994) 1232.
L. A. N. Amaral, A. L. Barabäsi, S. V. Buldyrev, S. Havlin and H. E. Stanley, preprint.
H. Leschhorn and L. H. Tang, Phys. Rev. E 49 (1994) 1238.
S. Roux and A. Hansen, J. Phys. I France, 4 (1994) 515.
M. Kolb, J.-F. Gouyet and B. Sapoval, Europhys. Letters 3 (1987) 33; M. Kolb, T. Gobron, J.-F. Gouyet and B. Sapoval, Europhys. Letters 11 (1990) 601.
S. Mazur and S. Reich, J. Phys. Chem., 90 (1986) 1365; R. P. Wool, B.-L. Yuan and O. J. McGarel, Poly. Eng. Sci. 29 (1989) 1340.
See for instance B. Sapoval, “A new approach to the linear and non-linear response of self similar electrodes, in “Chaos, Solitons and Factals”, Pergamon Pres., 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this paper
Cite this paper
Gouyet, J.F. (1994). Interface bursting and interface depinning. In: Pękalski, A. (eds) Diffusion Processes: Experiment, Theory, Simulations. Lecture Notes in Physics, vol 438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031123
Download citation
DOI: https://doi.org/10.1007/BFb0031123
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58653-1
Online ISBN: 978-3-540-49038-8
eBook Packages: Springer Book Archive