Statistical analysis of off-lattice diffusion-limited aggregates in channel and sector geometries

Abstract

The statistical properties of off-lattice diffusion-limited aggregates (DLA) grown in a strip between two reflecting walls are investigated. A large number of independent runs are performed and the cell occupancy distribution is measured and compared with the predictions of a recently proposed mean-field theory (MFT). It is shown that the mean occupancy profile moves at constant speed and has a shape and a selection mechanism similar to that of stable Saffman-Taylor fingers. In particular, there exists a specific contour line of the mean occupancy distribution (ρ=0.6${\mathrm{\rho }}_{\max }$) that has the width and the shape of the Saffman-Taylor finger λ=0.5. Motivated by the connection to the Saffman-Taylor problem, we extend our study to DLA growth in sector-shaped cells. Again a remarkable agreement is found between the mean occupancy profile and the shape of the selected stable finger in the small surface tension limit. Moreover, whenever the smooth finger is theoretically expected to undergo a tip-splitting instability, one observes, as predicted by the MFT, a qualitative change in the cell occupancy distribution that exhibits ‘‘profile crossing’’ together with a pronounced flattening of the tip region. We comment on this phenomenon, which was not observed in a previous similar statistical analysis of on-lattice DLA clusters due to the stabilizing effect of lattice anisotropy. The implications of our numerical results to the relevance of the DLA mean-field theory are discussed. © 1996 The American Physical Society.