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Distribution of dangling ends on the incipient percolation cluster

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  • Porto, Markus
  • Bunde, Armin
  • Havlin, Shlomo

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)∼M−(1+κ), with an exponent κ=dfB/df, where df and dfB are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield κ=0.83 in d=2 and κ=0.74 in d=3 in very good agreement with theory.

Suggested Citation

  • Porto, Markus & Bunde, Armin & Havlin, Shlomo, 1999. "Distribution of dangling ends on the incipient percolation cluster," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 96-99.
  • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:96-99 DOI: 10.1016/S0378-4371(98)00581-0
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    1. Quispel, G.R.W. & Capel, H.W. & Papageorgiou, V.G. & Nijhoff, F.W., 1991. "Integrable mappings derived from soliton equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 243-266.
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