Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
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 in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitätsbibliothek Leipzig
2015
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| Online Access: | http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190406 http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190406 http://www.qucosa.de/fileadmin/data/qucosa/documents/19040/diff_fund_11%282009%2959.pdf |
| Summary: | 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]. |
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