Mean-field diffusion-limited aggregation in radial geometries

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Abstract
We extend our study of a recently proposed mean-field theory (MFT) for diffusion-limited aggregation (DLA) to radial geometries. These include growth from a point in a fully open space and also growth in sectors with a range of opening angles. We find that the MFT accurately predicts the shape, angular width, and anisotropy dependence of the ensemble-averaged DLA pattern. For systems such that there is no stable solution of the related Saffman-Taylor problem, the mean-field theory exhibits an extreme flattening of the tip region which is also present in averaged DLA. The latter fact has not been noticed previously due to the stabilizing effect of lattice anisotropy present in previous simulations.

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