Competing Structures in DLA and Viscous Fingering

We summarize some recent work aiming at the characterization of coherent structures in unstable viscous fingering and diffusion-limited aggregation. A simplified needle model has been found which gives a good description of the probability field for n-fold symmetric anisotropic growth for small n. It is pointed out that it also explains why the aggregates have n equal branches for n 6. Isotropic growth has been investigated in confined and radial geometries. In confined geometries, the mean shape of aggregates and unstable viscous fingers is well described by the known classical smooth shapes. This is unfortunately not explained by a simple mean-field theory and the basic difficulties are summarized. In order to describe the growing structures in the radial geometry, the overlap between two growth sites is defined. This gives a quantitative measure of the notion that two growth sites belong to the same branch. For isotropic growth in the radial geometry, the average overlap is found to decrease with the number N of particles. This indicates that the number of branches increases with N. Moreover the overlap function and its fluctuations obey a scaling law suggesting that a mean branch shape exists in the limit N→∞ but that it fluctuates from aggregate to aggregate.