Fundamental problems concerning three dimensional clustering on surfaces

By extending the two dimensional theory of islanding by Marqusee to the case of three dimensional clustering on surfaces, we investigate the power law behaviour of average cluster radius as a function of time. We find that the average cluster radius asymptotically approaches the t1/4 behaviour predicted 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 cluster shape may explain the positive skewness and the widening of the size distribution which have been observed experimentally.