Diffusion-limited aggregation without branching: A detailed analysis

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Abstract
Diffusion-limited aggregation without branching is a model of diffusive growth in which tip splitting is absent. The resulting aggregates are sets of needles growing away from the initial deposition plane: They exhibit nontrivial scaling features. This paper contains a detailed study of the model. New results from computer simulations in two, three, and four dimensions are presented, and it is found that, for dimensions larger than 2, the value of the exponent controlling scaling becomes very close to the mean-field theory (continuum approximation) prediction. A theoretical treatment based on ideas close in spirit to real-space renormalization-group methods is discussed in detail. The analog of a Monte Carlo renormalization-group analysis based on this treatment is carried out, yielding predictions for the scaling exponent which agree well with simulation data.

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