Abstract
Irregular surfaces and interfaces are ubiquitous in nature. They exist on all scales from that of atoms to that of mountains. Their study requires three levels of consideration: (1) a description of their geometry, (2) an explanation of their existence, and (3) an understanding of their properties. Fractal geometry may play a role at all three of these levels.
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References
P. Pfeifer, M. Obert, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New-York 1989), p. 11
B.B. Mandelbrot: The Fractal Geometry of Nature (W.H. Freeman, New York 1982)
R. Voss, in: The Science of Fractal Images, ed. by H.P. Peitgen, D. Saupe (Springer, Berlin, Heidelberg 1988), p. 21
D. Saupe, in: The Science of Fractal Images, ed. by H.P. Peitgen, D. Saupe (Springer, Berlin, Heidelberg 1988), p. 71
C. R. Carme, private communication
M.W. Mitchell, D.A. Bonnell: J. Mater. Res. 5, 2251 (1990)
B.B. Mandelbrot, in: Fractals in Physics, ed. by L. Pietronero, E. Tossati (North-Holland, Amsterdam 1986), p. 3
J. Feder: Fractals (Plenum, New York 1988)
T. Vicsek: Fractal Growth Phenomena (World Scientific, Singapore 1989)
II.E. Hurst: Trans. Am. Soc. Civ. Eng. 116, 770 (1951)
F. Family, in: Universalities in Condensed Matter, ed. by R. Jullien, L. Peliti, R. Rammal, N. Boccara (Springer, Berlin, Heidelberg 1988), p. 193;
See also F. Family: Physica A 168, 561 (1990) (Proc. of the 3rd Bar-Ilan Conf. on Frontiers in Condensed Matter, Tel Aviv, January 1990)
R.F. Voss, in: Fundamental Algorithms in Computer Graphics, ed. by R.A. Earnshaw, (Springer, Berlin, Heidelberg 1985), p. 805
F. Family, T. Vicsek: J. Phys. A 18, L75 (1985)
J. Kertész, D.E. Wolf: Physica D 38, 221 (1989)
R. Messier, J.E. Yehoda: J. Appl. Phys. 58, 3739 (1985)
T. Hashimoto, K. Okamoto, K. Hara, M. Kamiya, II. Fujiwara: Thin Solids Films 91, 145 (1982)
H.J. Leamy, A.G. Dirks: J. Appl. Phys. 49, 3430 (1978)
H.J. Leamy, G.H. Gilmer, A.G. Dirks: Curr. Topics Mater. Sci. 6, 309 (1980)
O. Geszti, L. Gosztola, E. Seyfried: Thin Solid Films 136, L35 (1986)
M.J. Brett: J. Mater. Sci. Lett. 8, 415 (1989); see also Deposition Processes (parts I&II), MRS Bulletin 13, Nos. 11&12 (1988);
for a comparison with experiments, see R.N. Tait, T. Smy, M.J. Brett: Thin Solid Films 187, 375 (1990)
F. Family: J. Phys. A 19, L441 (1986)
S.F. Edwards, D.R. Wilkinson: Proc. R. Soc. London, A 381, 17 (1982)
M.J. Void: J. Coll. Science 14, 168 (1959)
P. Meakin, P. Ramanlal, L.M. Sander, R.C. Ball: Phys. Rev. A 34, 5091 (1986)
J. Krug, P. Meakin: Phys. Rev. A 40, 2064 (1989);
P. Meakin, J. Krug: Europhys. Lett. 11, 7 (1990)
N.G. Nakhodkin, A.I. Shadervan: Thin Solid Films 10, 109 (1972)
P. Meakin: Physica D 38, 252 (1989)
J.M. Kim, J.M. Kosterlitz: Phys. Rev. Lett. 62, 2289 (1989)
D. Dhar: Phase Transitions 9, 51 (1987)
A. Bunde, H.J. Herrmann, A. Margolina, H.E. Stanley: Phys. Rev. Lett. 55, 653 (1985)
E. Medina, T. Hwa, M. Kardar, Y. Zhang: Phys. Rev. A 39, 3053 (1989)
P. Meakin, R. Jullien: Europhys. Lett. 9, 71 (1989)
A. Margolina, H.E. Warriner: J. Stat. Phys. 60, 809 (1990)
M. Kardar, G. Parisi, Y.C. Zhang: Phys. Rev. Lett. 56, 889 (1986); Numerical solutions of the KPZ equation can be found in: J.G. Amar, F. Family: Phys. Rev. A 41, 3399 (1990)
W. Zdaniewski: J. Am. Ceram. Soc. 72, 116 (1989)
R. Desmaison, in: Protégeons la Montagne (Nathan, Paris 1978)
B.B. Mandelbrot, D.E. Passoja, A.J. Paulay: Nature 308, 721 (1984)
CS. Pande, L.R. Richards, S. Smith: J. Mater. Sci. Lett. 6, 295 (1987)
D.L. Davidson: J. Mater. Sci. 24, 681 (1989)
E. Bouchaud, G. Lapasset, J. Planes: Europhys. Lett. 13, 73 (1990)
L. de Arcangelis, A. Hansen, H.J. Herrmann, S. Roux: Phys. Rev. B 40, 877 (1989);
For d — 2 models of crack propagation see: P. Meakin, G. Li, L.M. Sander, E. Louis, F. Guinea: J. Phys. A 22, 1393 (1989) and
E.L. Hinrichsen, A. Hansen, S. Roux: Europhys. Lett. 8, 1 (1989)
E. Louis, F. Guinea, F. Flores, in: Fractals in Physics, ed. by L. Pietronero, E. Tossati (North-Holland, Amsterdam 1986), p. 177
E.E. Underwood, K. Banerji: Mater. Sci. Eng. 80, 1 (1986)
B. Sapoval, M. Rosso, J.F. Gouyet: J. de Phys. Lett. 46, L149 (1985)
B. Sapoval, M. Rosso, J.F. Gouyet, J.F. Colonna: Solid State Ionics 18&19, 21 (1986)
R.F. Voss: J. Phys. A 17, L51 (1984)
R. Ziff, B. Sapoval: J. Phys. A 19, L1169 (1986)
A. Bunde, J.F. Gouyet: J. Phys. A 18, L285 (1985)
H. Saleur, B. Duplantier: Phys. Rev. Lett. 58, 2325 (1987)
D. Stauffer: Introduction to Percolation Theory (Taylor & Francis, London 1985)
B. Sapoval, M. Rosso, J.F. Gouyet, Y. Boughaleb: Proc. of the 1988 Seminar on Fractals in Physics, Erice, Italy (Plenum, New York 1990);
B. Sapoval: Phil. Mag. B 59, 75 (1989);
J.F. Gouyet, Y. Boughaleb: Phys. Rev. B 40, 4760 (1989)
M Kolb, J.F. Gouyet, B. Sapoval: Europhys. Lett. 3, 33 (1987);
J.F. Gouyet: Solid State Ionics 28–30, 72 (1988);
M. Kolb, T. Gobron, J.F. Gouyet, B. Sapoval: Europhys. Lett. 11, 601 (1990)
S. Mazur, S. Reich: J. Phys. Chem. 90, 1365 (1986)
R.P. Wool, in: New Trends in Physics and Physical Chemistry of Polymers, ed. by Lieng-Huan Lee (Plenum, New York 1989), p. 129
M. Rosso, B. Sapoval, J.F. Gouyet: Phys. Rev. Lett. 57, 3195 (1986)
J.F. Gouyet, M. Rosso, B. Sapoval: Phys. Rev. B 37, 1832 (1988)
H. Van Damme, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New York 1989), p. 199
J. Nittmann, G. Daccord, H.E. Stanley: Nature 314, 141 (1985);
J. Nittmann, G. Daccord, H.E. Stanley, in: Fractals in Physics, ed. by L. Pietronero, E. Tossati (North-Holland, Amsterdam 1986), p. 193
J.D. Chen: Exp. Fluids, 5, 363 (1987)
H.J.S. Hele Shaw: Nature 58, 34 (1898)
F.A.L. Dullien: Porous Media: Fluid Transport and Pore Structure (Academic, London 1979)
P.M. Adler, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New York 1989), p. 341, and references therein
R. Vacher, T. Woigner, J. Pelous, E. Courtens: Phys. Rev. B 37, 6500 (1988);
F. Chaput, J.P. Boilot, A. Dauger, F. Devreux, A. de Geyer: J. Non-Cryst. Solids 116, 133 (1990)
C. Chachaty, J.P. Korb, J.R.C. Van der Maarel, W. Bras, P. Quinn: preprint (1991)
A.J. Katz, A.H. Thompson: Phys. Rev. Lett. 54, 1325 (1985)
D. Farin, D. Avnir, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New York 1989), p. 271, and references therein
E. Guyon, G.D. Mitescu, J.P. Hulin, S. Roux: Physica D 38, 172 (1989)
B. Sapoval, M. Rosso, J.F. Gouyet, in: The Fractal Approach to Heterogeneous Chemistry, ed. by D. Avnir (Wiley, New York 1989), p. 227
T.M. Shaw: Phys. Rev. Lett. 59, 1671 (1987)
R. Lenormand, C. Zarcone, A. Sarr: J. Fluid Mech. 135, 337 (1983)
R. Lenormand: C.R. Acad. Sci. Paris II 301, 247 (1985)
R. Lenormand, E. Touboul, C. Zarcone: J. Fluid Mech. 189, 165 (1988)
L. Paterson: Phys. Rev. Lett. 52, 1621 (1984)
P. Meakin, J.M. Deutch: J. Chem. Phys. 85, 2320 (1986)
D. Wilkinson, in: Physics of Finely Divided Matter, ed. by N. Boccara, M. Daoud (Springer, Berlin, Heidelberg 1985), p. 280
M. Cieplak, M.O. Robbins: Phys. Rev. Lett. 60, 2042 (1988)
M.A. Rubio, C.A. Edwards, A. Dougherty, J.P. Gollub: Phys. Rev. Lett. 63, 1685 (1989);
V.K. Horvath, F. Family, T. Viscek: J. Phys. A 24, L25 (1991)
T. Viscek, M. Cserzo, V.K. Horvath: Physica A 167, 315 (1990)
Y.-C. Zhang: J. de Phys. 51, 2113 (1990)
Y.-C. Zhang: Physica A 170, 1 (1990);
Y.-C. Zhang: J. Krug: J. de Phys. I 1, 9 (1991);
S. Havlin, S.V. Buldyrev, H.E. Stanley, G.H. Weiss: preprint (1991)
J.G. Amar, F. Family: J. Phys. A 24, L79 (1991);
S.V. Buldyrev, S. Havlin, J. Kertesz, H.E. Stanley, T. Viscek: Phys. Rev. A 43, (15 June 1991)
E. Clement, C. Baudet, E. Guyon, J.P. Hulin: J. Phys. D 20, 608 (1987);
See also J.-D. Chen, M.M. Dias, S. Platz, L.M. Schwartz: Phys. Rev. Lett. 61, 1489 (1988)
J.P. Hulin, E. Clement, C. Baudet, J.F. Gouyet, M. Rosso: Phys. Rev. Lett. 61, 333 (1988)
J.F. Gouyet, M. Rosso, E. Clément, C. Baudet, J.P. Hulin, in: Hydrodynamics of Dispersed Media, ed. by J.P. Hulin, A.M. Cazabat, E. Guyon, F. Carmona (Elsevier, Amsterdam 1990), p. 179
K.J. Mal0y, J. Feder, F. Boger, T. J0ssang: Phys. Rev. Lett. 61, 2925 (1988)
Y. Kantor, in: Statistical Mechanics of Membranes and Surfaces, Vol.5, ed. by D. Nelson, T. Piran, S. Weinberg (World Scientific, Singapore 1989), p. 115
A. Blumstein, R. Blumstein, T.H. Vanderspurt: J. Colloid Interface Sci. 31, 236 (1969)
J.II. Fendler, P. Tundo: Ace. Chem. Res. 17, 3 (1984)
R.M. Bradley: Phys. Rev. A 41, 914 (1990), and references therein
Y. Kantor, M. Kardar, D.R. Nelson: Phys. Rev. Lett. 57, 791 (1986)
D. Nelson, in: Statistical Mechanics of Membranes and Surfaces, Vol.5, ed. by D. Nelson, T. Piran, S. Weinberg (World Scientific, Singapore 1989), p. 1 and p. 137
B. Sapoval: Fractals (Aditech, Paris 1990)
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Gouyet, JF., Rosso, M., Sapoval, B. (1991). Fractal Surfaces and Interfaces. In: Bunde, A., Havlin, S. (eds) Fractals and Disordered Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51435-7_7
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DOI: https://doi.org/10.1007/978-3-642-51435-7_7
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