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Physical Review A
The qth moment M(q) of the growth probability of diffusion-limited aggregates is studied for q<0 in terms of the value [M(q,N)]av obtained by averaging M(q) over the ensemble of all aggregates of a given number of particles N. For a range of structures that are susceptible to precise analysis, we verify that all moments, even those for q<0, obey asymptotic power-law scaling in N. Since we cannot analyze completely arbitrary structures, our analysis is not definitive. However, it does suggest the validity of a recent proposal by one of us that there is no Lifshitz-like anomaly (similar to that found for the distribution of currents in the random resistor network) leading to non-power-law scaling of the negative moments of the growth probability.
Harris, A., & Cohen, M. (1990). Scaling of Negative Moments of the Growth Probability of Diffusion-Limited Aggregates. Physical Review A, 41 (2), 971-982. http://dx.doi.org/10.1103/PhysRevA.41.971
Date Posted: 12 August 2015
This document has been peer reviewed.