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A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and "edge adatoms" along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.

We introduce a model for epitaxial phenomena based on the motion of island boundaries, which is described by the level-set method. Our model treats the growing film as a continuum in the lateral direction, but retains atomistic discreteness in the growth direction. An example of such an ‘‘island dynamics’’ model using the level-set method is presented and compared with the corresponding rate equation description. Extensions of our methodology to more general settings are then discussed. @S1063-651X~98!50212-7#

Monte Carlo simulations and a scaling hypothesis are used to study the distribution of blob masses on two-dimensional finite-mass clusters at the percolation threshold. The exponents associated with this distribution function are a combination of backbone and percolation exponents. This work offers insights into the structure and fragmentation properties of percolation clusters in particular, and provides methods applicable to other fractal distribution problems in general.

Carlo computer simulations of spinodal decomposition to show that the model exhibits "pinning" of the structure factor, a behavior also seen in phase-separating polymer gels and binary alloys with impurities. The rate of strong bond formation depends on an entropic parameter 0, and we fInd both the pinned domain size and the crossover time between "normal" spinodal decomposition and the pinning scale with 0 as power laws with exponents that relate simply to the usual growth exponent. We propose a speci6c mechanism for pinning that permits the prediction of exact values for the pinning exponents. Finally, we discuss applications of the model to binary alloys with quenched disorder and polymer gels.