2010/12/02 by Markus Spanner, Felix Höfling, Gerd Schröder-Turk +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Anomalous diffusion #Conductivity #Critical point (mathematics) #Diffusion #Displacement (psychology) #Electrical resistivity and conductivity #Material Dynamics and Properties #Percolation (cognitive psychology) #Scaling #Stochastic processes and statistical mechanics #TRACER #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0953-8984/23/23/234120
published as J. Phys.: Condens. Matter 23, 234120 (2011)
arxiv created 2010/12/02 · openalex publication_date 2011/05/25 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.