For a continuum percolation model, it has been shown recentlythat the crossover from pure subdiffusion to normal diffusion extends over five decades in time [1, 2]; in addition, the asymptotic behavior is slowly approached and the large corrections cannot simply be ignored. Thus, it is of general interest to develop a systematic description of universal corrections to scaling in percolating systems.
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behavior at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker.
We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents [3].
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-190406 |
| Date | 03 December 2015 |
| Creators | Franosch, Thomas, Höfling, Felix |
| Contributors | Ludwig-Maximilians-Universität München, Fakultät für Physik, Universität Leipzig, Fakultät für Physik und Geowissenschaften |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:article |
| Format | application/pdf |
| Source | Diffusion fundamentals 11 (2009) 59, S. 1 |
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