Scaling in the Diffusion Limited Aggregation Model

Anton Menshutin
Phys. Rev. Lett. 108, 015501 – Published 3 January 2012

Abstract

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/Rdep(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/Rdep) function on an ensemble with 1000 clusters of 5×107 particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.

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  • Received 11 September 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.015501

© 2012 American Physical Society

Authors & Affiliations

Anton Menshutin

  • Landau Institute for Theoretical Physics and Scientific Center in Chernogolovka, 142432 Chernogolovka, Russia

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Issue

Vol. 108, Iss. 1 — 6 January 2012

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