Distribution of dangling ends on the incipient percolation cluster

Markus Porto, Armin Bunde, Shlomo Havlin

Research output: Contribution to journalConference articlepeer-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 = 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.

Original languageEnglish
Pages (from-to)96-99
Number of pages4
JournalPhysica A: Statistical Mechanics and its Applications
Volume266
Issue number1-4
DOIs
StatePublished - 15 Apr 1999
EventProceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications - Giessen, Ger
Duration: 14 Jul 199817 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.

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