Fundamental problems concerning three dimensional clustering on surfaces

By extending the two dimensional theory of islanding by Marqusee to the cas e of three dimensional clustering on surfaces, we investigate the power law behaviour of average cluster radius as a function of time. We find that th e average cluster radius asymptotically approaches the t(1/4) behaviour pre dicted in previous models which have been based on physically unreasonable assumptions. We discuss the effect of reshaping during cluster formation on surfaces on the expected cluster size distribution. A nonequilibrium clust er shape may explain the positive skewness and the widening of the size dis tribution which have been observed experimentally. (C) 1998 Elsevier Scienc e B.V. All rights reserved.