Article

The Localization Transition of the Two-Dimensional Lorentz Model

Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP UK; Max-Planck-Institut für Metallforschung, Heisenbergstraße 3, 70569 Stuttgart, Germany; Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany; Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
The European Physical Journal Special Topics (Impact Factor: 1.8). 03/2010; DOI: 10.1140/epjst/e2010-01313-1
Source: arXiv

ABSTRACT We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase. Comment: 13 pages, 7 figures.

0 Bookmarks
 · 
101 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.
    Reports on Progress in Physics 03/2013; 76(4):046602. · 13.23 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: ... JP Wittmer ( ) · JE Zabel · P. Polinska · N. Schulmann · H. Meyer · J . Farago · A. Johner · J . Baschnagel Institut Charles Sadron, Université de Strasbourg, CNRS, 23 rue du Loess, 67037 Strasbourg Cedex, France e-mail: joachim. wittmer @ics-cnrs.unistra.fr ... JP Wittmer et al. ...
    Journal of Statistical Physics 11/2011; 145(4):1017-1126. · 1.40 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we find delocalized tracer particle dynamics at small matrix area fractions and localized motion of the tracers at high matrix area fractions. In the delocalized region, the dynamics is subdiffusive at intermediate times, and diffusive at long times, while in the localized regime, trapping in finite pockets of the matrix is observed. These observations are found to agree with the simulation of an ideal gas confined in a weakly correlated matrix. Our results show that Lorentz gas systems with soft interactions are exhibiting a smoothening of the critical dynamics and consequently a rounded delocalization-to-localization transition.
    Physical Review Letters 09/2013; 111(12):128301. · 7.73 Impact Factor

Full-text (2 Sources)

Download
46 Downloads
Available from
May 31, 2014

Felix Höfling