TRANSPARENT DIFFUSION-LIMITED AGGREGATION IN ONE-DIMENSION

We introduce a transparent version of diffusion-limited aggregation (D LA) wherein the walkers stick to the aggregate with probability mu les s than unity and are allowed to penetrate the aggregate. We study this model in one spatial dimension. We show that the ensemble average of this process is in the steady state only when one takes the average in the instantaneous frame of the lead particle. We calculate this avera ge exactly for mu near one. For small sticking probability, we introdu ce a mean-field treatment. As opposed to the standard mean-field treat ments of DLA, our version, based on our novel ensemble average, shows no singular behaviour and no need for ad-hoc cut-off procedures. This mean-field treatment in quantitatively accurate as long as mu is not t oo small and qualitatively correct for all mu. We discuss the quantita tive breakdown of the mean-field treatment for very small mu and direc tions towards improvement. The implications of these findings and futu re directions for research are also discussed.