Cluster-Resolved Dynamic Scaling Theory and Universal Corrections for Transport on Percolating Systems

Abstract

<lb>For a continuum percolation model, it has been shown recently that the crossover<lb>from pure subdiffusion to normal diffusion extends over five decades in time [1, 2]; in<lb>addition, the asymptotic behavior is slowly approached and the large corrections cannot<lb>simply be ignored. Thus, it is of general interest to develop a systematic description of<lb>universal corrections to scaling in percolating systems. For percolating systems, we<lb>propose a universal exponent relation connecting the leading corrections to scaling of the<lb>cluster size distribution with the dynamic corrections to the asymptotic transport behavior<lb>at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the<lb>scaling of both the cluster size distribution and the dynamics of a random walker.<lb>We corroborate our theoretical approach by extensive simulations for a site<lb>percolating square lattice and numerically determine both the static and dynamic<lb>correction exponents [3]. References<lb>[1] F. Höfling, T. Franosch, and E. Frey, Phys. Rev. Lett. 96 (2006) 165901.<lb>[2] F. Höfling, T. Munk, E. Frey, and T. Franosch, J. Chem. Phys. 128 (2008) 164517.<lb>[3] A. Kammerer, F. Höfling, and T. Franosch, EPL 84 (2008) 66002.<lb>The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application © 2009, T. Franosch<lb>diffusion-fundamentals.org 11 (2009) 59, pp 1-1

Cite this paper

@inproceedings{Franosch2008ClusterResolvedDS, title={Cluster-Resolved Dynamic Scaling Theory and Universal Corrections for Transport on Percolating Systems}, author={Thomas Franosch and Felix H{\"{o}fling and Arnold Sommerfeld}, year={2008} }