### Abstract

The structure of fjords in diffusion-limited aggregation (DLA) clusters can be described in terms of the loop size distribution n_{R}(x) which is the normalised number of loops with a neck to depth ratio x within a circle of radius R centred at the origin of the cluster. The authors find from the numerical study of very large off-lattice aggregates that n_{R}(x) converges quickly to a limiting distribution with a well defined smallest ratio x_{min} larger than zero indicating the self-similarity of the loop structure. If the fjords are self-similar, i.e. they do not have long, tube-like structures, one does not expect a phase transition in the multifractal spectrum of growth probabilities of typical DLA clusters generated on the plain. Their study is essentially statistical and they cannot rule out the possibility of such 'rare events' (e.g. the occurrence of a few loops with anomalously small x) which may result in a qualitatively different behaviour concerning the multifractal spectrum.

Original language | English |
---|---|

Article number | 007 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 23 |

Issue number | 15 |

DOIs | |

Publication status | Published - 1990 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*23*(15), [007]. https://doi.org/10.1088/0305-4470/23/15/007

**Self-similarity of the loop structure of diffusion-limited aggregates.** / Barabasi, Albert L.; Vicsek, T.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 23, no. 15, 007. https://doi.org/10.1088/0305-4470/23/15/007

}

TY - JOUR

T1 - Self-similarity of the loop structure of diffusion-limited aggregates

AU - Barabasi, Albert L.

AU - Vicsek, T.

PY - 1990

Y1 - 1990

N2 - The structure of fjords in diffusion-limited aggregation (DLA) clusters can be described in terms of the loop size distribution nR(x) which is the normalised number of loops with a neck to depth ratio x within a circle of radius R centred at the origin of the cluster. The authors find from the numerical study of very large off-lattice aggregates that nR(x) converges quickly to a limiting distribution with a well defined smallest ratio xmin larger than zero indicating the self-similarity of the loop structure. If the fjords are self-similar, i.e. they do not have long, tube-like structures, one does not expect a phase transition in the multifractal spectrum of growth probabilities of typical DLA clusters generated on the plain. Their study is essentially statistical and they cannot rule out the possibility of such 'rare events' (e.g. the occurrence of a few loops with anomalously small x) which may result in a qualitatively different behaviour concerning the multifractal spectrum.

AB - The structure of fjords in diffusion-limited aggregation (DLA) clusters can be described in terms of the loop size distribution nR(x) which is the normalised number of loops with a neck to depth ratio x within a circle of radius R centred at the origin of the cluster. The authors find from the numerical study of very large off-lattice aggregates that nR(x) converges quickly to a limiting distribution with a well defined smallest ratio xmin larger than zero indicating the self-similarity of the loop structure. If the fjords are self-similar, i.e. they do not have long, tube-like structures, one does not expect a phase transition in the multifractal spectrum of growth probabilities of typical DLA clusters generated on the plain. Their study is essentially statistical and they cannot rule out the possibility of such 'rare events' (e.g. the occurrence of a few loops with anomalously small x) which may result in a qualitatively different behaviour concerning the multifractal spectrum.

UR - http://www.scopus.com/inward/record.url?scp=5344241971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5344241971&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/23/15/007

DO - 10.1088/0305-4470/23/15/007

M3 - Article

AN - SCOPUS:5344241971

VL - 23

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 15

M1 - 007

ER -