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Updated: Jun 1, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Anomalous transport of a tracer on percolating clusters
Markus Spanner1, Felix Höfling, Gerd E Schröder-Turk
1Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany.
Abstract:
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as a response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.
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