Spontaneous generation of discrete scale invariance in growth models

Abstract

We suggest that the short-wavelength Mullins-Sekerka instability, together with strong screening effects, generate spontaneously a discrete scale invariance (DSI) in growth processes. A signature of this DSI is the presence of log-periodic oscillations correcting the usual power laws. This is confirmed by extensive numerical simulations on the needle model, using various growth rules (diffusion-limited aggregation, angle screening, η model, and crack approximation) on systems containing up to 5000 needles, and by some experimental data on geological cracks.