A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model
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 simil...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2011-06-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/18/381/2011/npg-18-381-2011.pdf |
| _version_ | 1818290262719332352 |
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| author | S. Hergarten R. Krenn |
| author_facet | S. Hergarten R. Krenn |
| author_sort | S. Hergarten |
| collection | DOAJ |
| description | 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 <i>τ</i> of the event size distribution directly from the scaling of the accessible perimeter of percolation clusters. We obtain <i>&tau;</i> = 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. |
| first_indexed | 2024-12-13T02:25:23Z |
| format | Article |
| id | doaj.art-7848e03fb54a44a480ed813cdfb2a7e8 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-12-13T02:25:23Z |
| publishDate | 2011-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-7848e03fb54a44a480ed813cdfb2a7e82022-12-22T00:02:39ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462011-06-0118338138810.5194/npg-18-381-2011A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire modelS. HergartenR. KrennWe 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 <i>τ</i> of the event size distribution directly from the scaling of the accessible perimeter of percolation clusters. We obtain <i>&tau;</i> = 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.http://www.nonlin-processes-geophys.net/18/381/2011/npg-18-381-2011.pdf |
| spellingShingle | S. Hergarten R. Krenn A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model Nonlinear Processes in Geophysics |
| title | A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| title_full | A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| title_fullStr | A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| title_full_unstemmed | A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| title_short | A semi-phenomenological approach to explain the event-size distribution of the Drossel-Schwabl forest-fire model |
| title_sort | semi phenomenological approach to explain the event size distribution of the drossel schwabl forest fire model |
| url | http://www.nonlin-processes-geophys.net/18/381/2011/npg-18-381-2011.pdf |
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