Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 27: Transport and Anomalous Diffusion
DY 27.9: Talk
Thursday, March 29, 2012, 16:45–17:00, MA 004
Space-resolved Dynamics in a Simple Porous Media Model — •Markus Spanner1, Simon Schnyder2, Thomas Voigtmann3, and Thomas Franosch1 — 1Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany — 2Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany — 3Institut für Materialphysik im Weltraum, DLR, 51170 Köln, Germany and Zukunftskolleg, Universität Konstanz, 78457 Konstanz, Germany
The Lorentz model is a simple model for transport in porous materials, where a point-like tracer explores the space between an array of quenched spherical obstacles. It was shown in previous computer simulations, that in the vicinity of the localization transition, the remaining void space becomes fractal, thus transport is drastically hindered and anomalous dynamics emerges. When considering only trajectories on the infinite cluster, sub-diffusive motion δ r∞2∼ t2/dw is found to follow an exponent of dw=4.81, known as the walk dimension.
Employing further extensive molecular dynamics simulation, both for ballistic and Brownian motion, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model in terms of the intermediate scattering functions. Covering different time and length scales simultaneously, these functions are sensitive to both the underlying spatial fractal and the anomalous transport.
We compare our simulation results close to the critical density to a mode-coupling approach, and find that certain aspects are surprisingly well predicted.