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| Titel |
A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| VerfasserIn |
S. Hergarten, R. Krenn |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 18, no. 3 ; Nr. 18, no. 3 (2011-06-21), S.381-388 |
| Datensatznummer |
250013924
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| Publikation (Nr.) |
 copernicus.org/npg-18-381-2011.pdf |
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| Zusammenfassung |
| We present a novel approach to explain the complex scaling behavior of the
Drossel-Schwabl forest-fire model in two dimensions. Clusters of trees are characterized
by their size and perimeter only, whereas spatial correlations
are neglected. Coalescence of clusters is restricted to clusters
of similar sizes. Our approach derives the value of the scaling exponent
τ of the event size distribution directly from
the scaling of the accessible perimeter of percolation clusters. We obtain
τ = 1.19 in the limit of infinite growth rate, in perfect agreement
with numerical results.
Furthermore, our approach predicts the unusual transition from a
power law to an exponential decay even quantitatively, while the exponential decay at
large event sizes itself is reproduced only qualitatively. |
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