SPONTANEOUS GENERATION OF DISCRETE SCALE-INVARIANCE IN GROWTH-MODELS

We suggest that the short-wavelength Mullins-Sekerka instability, toge ther 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 need le model, using various growth rules (diffusion-limited aggregation, a ngle screening, eta model, and crack approximation) on systems contain ing up to 5000 needles, and by some experimental data on geological cr acks.