Abstract
There is a class of pattern forming phenomena which can be described by the Laplace equation where the nonlinearity comes into the problem because of the moving boundary (which is the pattern itself). Many examples have been mentioned at this school; without seeking completeness we give a few references: the Saffman-Taylor instability,1 dielectric breakdown,2 flow through porous media3 or dendritic crystal growth.4 Here we want to deal with the last problem, but it should be emphasized that-mutatis mutandis-our method can be applied to different problems too.
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J. Nittmann, G. Daccord, and H. E. Stanley, Nature 314, 141 (1985).
L. Niemeyer, L. Pietronero, and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033. (1984).
L. Paterson, Phys. Rev. Lett. 52, 1621 (1984).
J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).
E. Ben-Jacob, N. Goldenfeld, J. S. Langer,, G. Schon, Phys. Rev. Lett. 51, 1930 (1983).
T. Vicsek, Phys. Rev. Lett. 53, 2281 (1984).
D. A. Kessler, J. Koplik and H. Levine, Phys. Rev. B30, 2820 (1984).
J. Szep, J. Cserti and J. Kertesz, J. Phys. A 18, L413 (1985).
P. R. Garabedian, Partial Differential Equations ( Wiley, NY, 1964 ) p 483.
L. P. Kadanoff, J. Stat. Phys. 39, 267 (1985).
T. A. Witten and L. M. Sander, Phys Rev. Lett. 47, 1400 (1981).
T. A. Witten and L. M. Sander, Phys. Rev. B 27, 5686 (1983).
P. Meakin, Phys. Rev. A 27, 2616 (1983).
Z. Racz, T. Vicsek, Phys Rev. Lett. 51, 2382 (1984).
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© 1986 Martinus Nijhoff Publishers, Dordrecht
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Kertèsz, J., Szèp, J., Cserti, J. (1986). Dendritic Growth by Monte Carlo. In: Stanley, H.E., Ostrowsky, N. (eds) On Growth and Form. NATO ASI Series, vol 100. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5165-5_22
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DOI: https://doi.org/10.1007/978-94-009-5165-5_22
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