TY - JOUR

T1 - Analytic solution of the growth-site probability distribution for structural models of diffusion-limited aggregation

AU - Lee, Jysoo

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

PY - 1992

Y1 - 1992

N2 - We present an analytic solution of the growth-site probability distribution for a family of hierarchical models for the structure of diffusion-limited aggregation (DLA) clusters. These models are characterized by self-similar voids that are delineated by narrow channels. The growth-site probability distributions for all the models are shown to have the same form, n(M)exp{-(A/lnM)[-0(M)]2}, where n(M)d is the number of growth sites with <-lnpi/lnM<+d, pi is the growth probability at site i, M is the cluster mass, 0(M)==B lnM, and A,B are constants. We find the same form of the distribution for all members of the family of models, suggesting the possibility that it is a consequence of the channels and self-similar voids, and is independent of other details of the model. Our result is in accord with the recent calculations for DLA clusters by Schwarzer et al. [Phys. Rev. A 43, 1134 (1991)].

AB - We present an analytic solution of the growth-site probability distribution for a family of hierarchical models for the structure of diffusion-limited aggregation (DLA) clusters. These models are characterized by self-similar voids that are delineated by narrow channels. The growth-site probability distributions for all the models are shown to have the same form, n(M)exp{-(A/lnM)[-0(M)]2}, where n(M)d is the number of growth sites with <-lnpi/lnM<+d, pi is the growth probability at site i, M is the cluster mass, 0(M)==B lnM, and A,B are constants. We find the same form of the distribution for all members of the family of models, suggesting the possibility that it is a consequence of the channels and self-similar voids, and is independent of other details of the model. Our result is in accord with the recent calculations for DLA clusters by Schwarzer et al. [Phys. Rev. A 43, 1134 (1991)].

UR - http://www.scopus.com/inward/record.url?scp=35949005549&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.45.1035

DO - 10.1103/PhysRevA.45.1035

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AN - SCOPUS:35949005549

SN - 2469-9926

VL - 45

SP - 1035

EP - 1043

JO - Physical Review A

JF - Physical Review A

IS - 2

ER -