STATISTICAL-ANALYSIS OF OFF-LATTICE DIFFUSION-LIMITED AGGREGATES IN CHANNEL AND SECTOR GEOMETRIES

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 occupan cy distribution is measured and compared with the predictions of a rec ently proposed mean-field theory (MFT). It is shown that the mean occu pancy profile moves at constant speed and has a shape and a selection mechanism similar to that of stable Saffman-Taylor fingers. In particu lar, there exists a specific contour line of the mean occupancy distri bution (rho=0.6 rho(max)) that has the width and the shape of the Saff man-Taylor finger lambda=0.5. Motivated by the connection to the Saffm an-Taylor problem, we extend our study to DLA growth in sector-shaped cells. Again a remarkable agreement is found between the mean occupanc y profile and the shape of the selected stable finger in the small sur face tension limit. Moreover, whenever the smooth finger is theoretica lly expected to undergo a tip-splitting instability, one observes, as predicted by the MFT, a qualitative change in the cell occupancy distr ibution 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 mea n-field theory are discussed.