Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Brownian Motion, Stochastic Processes, Transport II
DY 41.9: Talk
Friday, March 18, 2011, 12:30–12:45, HÜL 186
Subdiffusive transport on the infinite cluster of the Lorentz Model — •Markus Spanner1, Felix Höfling2, Gerd Schröder-Turk1, Klaus Mecke1, and Thomas Franosch1 — 1Theoretische Physik 1, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen — 2MPI für Metallforschung, Heisenbergstr. 3, und Institut für Theoretische und Angewandte Physik, Pfaffenwaldring 57, 70569 Stuttgart
The Lorentz model is a model for transport in porous materials, where a point-like tracer moves through an array of quenched spherical obstacles. Extensive simulations of this model were performed recently, and revealed anomalous transport at the void-space percolation transition. These studies considered all-cluster-averaged quantities, yet for deeper insight one would like to resolve the motion on the various clusters.
We conducted simulations of particles confined to the ‘infinite’ cluster, i.e. the fraction of void space that percolates through the system of obstacles, identified using a Voronoi tessellation. We find that the motion stays subdiffusive δ r∞2(t) ∼ t2/dw with a new exponent dw=4.81 known as walk dimension in the context of random walks in lattice percolation. Besides measuring the volume of the infinite cluster as a function of the obstacle density for systems of overlapping spheres, a detailed analysis of transport on this infinite cluster was carried out, including the vanishing of the diffusion coefficient near the transition, the non-gaussian parameter, the influence of finite system sizes and an extrapolation of the critical density from the dynamics. In contrast to the all-cluster-averaged dynamics, we observe a gaussian behavior for long times for densities below the localization threshold.