Surfaces, interfaces, and screening of fractal structures

Abstract

Fractal objects strongly screen external fields; only a small ‘‘surface’’ portion of the object is exposed appreciably to the field. We have studied this exposed surface of several random fractals as measured by random walkers and by ballistic particles launched from outside and absorbed by the fractal. The number of absorbing sites weighted by their rate of absorption shows an apparent power-law scaling with fractal mass. For diffusion-limited aggregates, ballistically generated aggregates, and screened-growth clusters in two dimensions, this power-law relationship is for the most part in accord with mean-field predictions of previous work. This accord is poorest for the objects of lowest fractal dimensionality. We have confirmed that this scaling is different from that of the old-growth–new-growth interface studied previously. We also find that a ‘‘hierarchy’’ of fractal dimensions describes the external surface of diffusion-limited aggregates.