Numéro
J. Phys. I France
Volume 6, Numéro 7, July 1996
Page(s) 949 - 967
DOI https://doi.org/10.1051/jp1:1996109
DOI: 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-Krumbhaar

Institut 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.



© Les Editions de Physiques 1996

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.