Renewal-anomalous-heterogeneous files

Abstract

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres' diffusion coefficients are distributed and the initial spheres' density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is exponential as in Brownian files, yet obeys: ψ_α (t)~t^(-1-α), 0<α<1. The file is renewal as all the particles attempt to jump at the same time. It is shown that the mean square displacement (MSD) in a renewal-anomalous-heterogeneous file, <r^2>, obeys, <r^2>~[<r^2>_{nrml}]^α, where <r^2 >_{nrml} is the MSD in the corresponding Brownian file. This scaling is an outcome of an exact relation (derived here) connecting probability density functions of Brownian files and renewal-anomalous files. It is also shown that non-renewal-anomalous files are slower than the corresponding renewal ones.

Accepted for publication (August, 2010)

References in corpus (5)

• From random walk to single-file diffusion
• Single-File diffusion in a Box
• Single File Diffusion enhancement in a fluctuating modulated 1D channel
• Strong Mobility in Weakly Disordered Systems
• Dynamics of heterogeneous hard spheres in a file

Cited by in corpus (4)

• Dynamics of heterogeneous hard spheres in a file
• Clustering in anomalous files of independent particles
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions