Stationary Growth and Unique Invariant Harmonic Measure of Cylindrical Diffusion Limited Aggregation
Riccardo Marchetti, Alessandro Taloni, Emanuele Caglioti, Vittorio Loreto, L. Pietronero · Physical Review Letters · 2012
We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (DLA) growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality, and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on a lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.