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 language | English |
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Pages (from-to) | 96-99 |
Number of pages | 4 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 266 |
Issue number | 1-4 |
DOIs | |
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 | Funder number |
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Alexander-von-Humboldt Foundation | |
Deutsche Forschungsgemeinschaft | |
German-Israeli Foundation for Scientific Research and Development |