Discontinuous Transition between Seaweed and Chaotic Growth Morphology

(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.