Diffusion-limited aggregation as a growth process statistically invariant under an infinitesimal affine transformation of mass and multiple spatial coordinates

Abstract

This work has two major results. First, it proposes a model of diffusion-limited aggregation (DLA) that accounts for the diversity of mass dependence exponents of four characteristic lengths: radius of gyration, major and minor asymmetry axes, and width of active growth zone. Second, it uses the agreement of model predictions with simulation data to show that the invariance of DLA growth probability under an infinitesimal affine transformation of mass and several growth zone spatial coordinates is consistent with the results of simulation data, to a high degree of approximation, in the range of aggregate mass from 200 to 50 000 for the first three of the above characteristic lengths, and in the range 1100\char21{}440 000 for the active zone width.