Fractal structures from an evaporation/condensation model

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Abstract
Several simple evaporation/condensation models in which all occupied surface sites have the same evaporation probability and condensation occurs on contact with the first occupied site have been investigated using Monte Carlo simulations. In two dimensional simulations these models generate a ‘‘cloud’’ of clusters which at long times are characterized by a fractal-like geometry and an exponential cluster size distribution. The nature of the systems at long times depends on the type of trajectories which the particles follow. Brownian trajectories lead to a cloud of clusters with a fractal dimensionality close to 1.0 (in 2D simulations), whereas linear trajectories generate structures with a fractal dimensionality close to 4/3. In similar one dimensional simulations, there is no evidence for the formation of fractal-like structures at any stage in the evolution of the systems and the equilibrium state consists of a dense region and a completely unoccupied region. The results of three dimensional simulations are inconclusive.