Diffusion-Limited Aggregation with a Restriction on the Growth Direction

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  • Diffusion Limited Aggregation with a

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A new type of two-dimensional diffusion-limited aggregation (DLA) is computer-simulated, in which the growth direction is restricted by the scale-invariant boundary. The seed particle from which the DLA cluster grows is located at the corner of a wedge-type boundary with the angle 90°. Two boundary conditions on the wedge are used; (a) absorption-type and (b) reflection-type. The average cluster length L along the bisector of the wedge and width W perpendicular to it are found to be scaled as L∼Nν⁄⁄ and W∼Nν⊥ for large N, where N is the total number of aggregated particles in the DLA cluster. It is also found that ν⁄⁄≅ν⊥ even for the absorption-type boundary condition which yields anisotropic diffusion field, although the clusters are more elongated (A≡L⁄W>1) than those for the reflection-type (A≅1).

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