Fractal models for diffusion controlled aggregation

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Abstract
A two-dimensional fractal model is constructed for diffusion controlled deposition on a surface. The fractal geometry of the deposit and the power law behaviour of the quantities characterising the non-equilibrium cluster size distribution are shown to be consequences of the competition generally present in a nonlinear growth process. A qualitative agreement with previous numerical results is found and the scaling laws for the critical exponents of the problem are shown to be satisfied exactly.

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