Issue |
J. Phys. I France
Volume 6, Number 7, July 1996
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Page(s) | 949 - 967 | |
DOI | https://doi.org/10.1051/jp1:1996109 |
J. Phys. I France 6 (1996) 949-967
Discontinuous Transition between Seaweed and Chaotic Growth Morphology
T. Ihle and H. Müller-KrumbhaarInstitut für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany
(Received 21 March 1995, revised 18 January 1996, accepted 27 March 1996)
Abstract
We study an interface moving in a diffusion-field in the high-speed region around unit-supercooling. A tunable relaxation
term in the diffusion equation allows us to obtain non-singular stationary solutions for arbitrary growth rate. We find a
change-over between KPZ and Kuramoto-Sivashinsky type behavior, and a discontinuous transition between the latter and compact
seaweed growth morphology which develops logarithmic singularities in finite time in qualitative agreement with computer simulations
of the fully time dependent moving boundary problem in two dimensions. A special multiple-scale analysis near absolute stability
yields an equation for the interface profile which reduces to the Kuramoto-Sivashinsky equation and an equation known from
directional solidification in some limit.
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