Distribution of dangling ends on the incipient percolation cluster

Markus Porto; Armin Bunde; Shlomo Havlin

doi:10.1016/S0378-4371(98)00581-0

Distribution of dangling ends on the incipient percolation cluster

Markus Porto
, Armin Bunde
, Shlomo Havlin

Department of Physics - at Bar-Ilan University

Justus Liebig University Giessen
Bar-Ilan University

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M) approx. M^-(1+k), with an exponent k = d_f^B/d_f, where d_f and d_f^B are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k = 0.83 in d = 2 and k = 0.74 in d = 3 in very good agreement with theory.

Original language	English
Pages (from-to)	96-99
Number of pages	4
Journal	Physica A: Statistical Mechanics and its Applications
Volume	266
Issue number	1-4
DOIs	https://doi.org/10.1016/S0378-4371(98)00581-0
State	Published - 15 Apr 1999
Event	Proceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications - Giessen, Ger Duration: 14 Jul 1998 → 17 Jul 1998

Bibliographical note

Funding Information:
This work was supported by the German-Israeli Foundation, the Minerva Center for the Physics of Mesoscopics, Fractals and Neural Networks; the Alexander-von-Humboldt Foundation; and the Deutsche Forschungsgemeinschaft.

Funding

This work was supported by the German-Israeli Foundation, the Minerva Center for the Physics of Mesoscopics, Fractals and Neural Networks; the Alexander-von-Humboldt Foundation; and the Deutsche Forschungsgemeinschaft.

Funders
Alexander-von-Humboldt Foundation
Deutsche Forschungsgemeinschaft
German-Israeli Foundation for Scientific Research and Development

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10.1016/S0378-4371(98)00581-0

Cite this

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title = "Distribution of dangling ends on the incipient percolation cluster",

abstract = "We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M) approx. M-(1+k), with an exponent k = dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k = 0.83 in d = 2 and k = 0.74 in d = 3 in very good agreement with theory.",

author = "Markus Porto and Armin Bunde and Shlomo Havlin",

note = "Funding Information: This work was supported by the German-Israeli Foundation, the Minerva Center for the Physics of Mesoscopics, Fractals and Neural Networks; the Alexander-von-Humboldt Foundation; and the Deutsche Forschungsgemeinschaft. ; Proceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications ; Conference date: 14-07-1998 Through 17-07-1998",

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AU - Bunde, Armin

AU - Havlin, Shlomo

N1 - Funding Information: This work was supported by the German-Israeli Foundation, the Minerva Center for the Physics of Mesoscopics, Fractals and Neural Networks; the Alexander-von-Humboldt Foundation; and the Deutsche Forschungsgemeinschaft.

PY - 1999/4/15

Y1 - 1999/4/15

N2 - We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M) approx. M-(1+k), with an exponent k = dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k = 0.83 in d = 2 and k = 0.74 in d = 3 in very good agreement with theory.

AB - We study numerically and by scaling arguments the probability P(M) dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M) approx. M-(1+k), with an exponent k = dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k = 0.83 in d = 2 and k = 0.74 in d = 3 in very good agreement with theory.

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Y2 - 14 July 1998 through 17 July 1998

ER -

Distribution of dangling ends on the incipient percolation cluster

Abstract

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