Multifractal scaling of 3D diffusion-limited aggregation

Stefan Schwarzer; Shlomo Havlin; H. Eugene Stanley

doi:10.1016/0378-4371(92)90514-Q

Multifractal scaling of 3D diffusion-limited aggregation

Stefan Schwarzer, Shlomo Havlin, H. Eugene Stanley

Department of Physics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the multifractal (MF) properties of the set of growth probabilities {p_i} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {p_i} display MF scaling for all moments-in contrast to 2D DLA, where one observes a "phase transition" in the MF spectrum for negative moments; (ii) multifractality is also displayed by the p_i located in a shell of reduced radius x ≡ r R_g, where R_g is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value α_av of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.

Original language	English
Pages (from-to)	117-122
Number of pages	6
Journal	Physica A: Statistical Mechanics and its Applications
Volume	191
Issue number	1-4
DOIs	https://doi.org/10.1016/0378-4371(92)90514-Q
State	Published - 15 Dec 1992

Bibliographical note

Funding Information:
We would like to thank P. Meakin for useful discussionsa nd for supplying cluster coordinates. We further thank M. Gyure, G. Huber, H. Larralde, S. Sastry, T. Udale, T. Vicsek and M. Wolf for comments and discussions. Financial support from NSF is gratefully acknowledged.

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title = "Multifractal scaling of 3D diffusion-limited aggregation",

abstract = "We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a {"}phase transition{"} in the MF spectrum for negative moments; (ii) multifractality is also displayed by the pi located in a shell of reduced radius x ≡ r Rg, where Rg is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value αav of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.",

author = "Stefan Schwarzer and Shlomo Havlin and Stanley, {H. Eugene}",

note = "Funding Information: We would like to thank P. Meakin for useful discussionsa nd for supplying cluster coordinates. We further thank M. Gyure, G. Huber, H. Larralde, S. Sastry, T. Udale, T. Vicsek and M. Wolf for comments and discussions. Financial support from NSF is gratefully acknowledged.",

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AU - Schwarzer, Stefan

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

N1 - Funding Information: We would like to thank P. Meakin for useful discussionsa nd for supplying cluster coordinates. We further thank M. Gyure, G. Huber, H. Larralde, S. Sastry, T. Udale, T. Vicsek and M. Wolf for comments and discussions. Financial support from NSF is gratefully acknowledged.

PY - 1992/12/15

Y1 - 1992/12/15

N2 - We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a "phase transition" in the MF spectrum for negative moments; (ii) multifractality is also displayed by the pi located in a shell of reduced radius x ≡ r Rg, where Rg is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value αav of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.

AB - We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a "phase transition" in the MF spectrum for negative moments; (ii) multifractality is also displayed by the pi located in a shell of reduced radius x ≡ r Rg, where Rg is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value αav of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.

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IS - 1-4

ER -

Multifractal scaling of 3D diffusion-limited aggregation

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