CONTINUUM MODEL FOR RADIAL INTERFACE GROWTH

A stochastic partial differential equation along the lines of the Kard ar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as r adially symmetric solutions are identified in the deterministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in the continuum in favour of the symmetric solutions. The asymptotic surface width scaling for s tochastic radial interface growth is investigated through numerical si mulations and found to be characterized by the same scaling exponent a s that for stochastic growth on a substrate. (C) 1998 Elsevier Science B.V. All rights reserved.