The sol-gel transition modelled by irreversible aggregation of clusters

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Abstract
Irreversible aggregation of clusters leads in a natural way to the formation of large ramified structures. We investigate this growth process close to the sol-gel transition, where for the first time an infinite spanning cluster appears, and find scaling behaviour. The kinetics of the model leads to properties which are distinct from standard percolation. Two critical exponents are determined numerically. The fractal dimension of the clusters is 0, = 1.75 f 0.07 in two dimensions.

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