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Article overview
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Minimal spanning trees at the percolation threshold: a numerical calculation | | Sean M. Sweeney
; A. Alan Middleton
; | | Date: |
29 Jun 2013 | | Abstract: | The fractal dimension of minimal spanning trees on percolation clusters is
estimated for dimensions $d$ up to $d=5$. A robust analysis technique is
developed for correlated data, as seen in such trees. This should be a robust
method suitable for analyzing a wide array of randomly generated fractal
structures. The trees analyzed using these techniques are built using a
combination of Prim’s and Kruskal’s algorithms for finding minimal spanning
trees. This combination reduces memory usage and allows for simulation of
larger systems than would otherwise be possible. The path length fractal
dimension $d_{s}$ of MSTs on critical percolation clusters is found to be
compatible with the predictions of the perturbation expansion developed by
T.S.Jackson and N.Read [T.S.Jackson and N.Read, Phys. Rev. E extbf{81},
021131 (2010)]. | | Source: | arXiv, 1307.0043 | | Services: | Forum | Review | PDF | Favorites | |
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