Anomalous Diffusion with Absorbing Boundary

TL;DR

This paper investigates sub-diffusive behavior of a Gaussian polymer with absorbing boundaries, highlighting differences from fractional Fokker-Planck models and showing finite mean absorption times.

Contribution

It provides a detailed analysis of anomalous diffusion with absorbing boundaries, revealing key distinctions from existing fractional Fokker-Planck descriptions.

Findings

Mean absorption time between two boundaries is finite.

Differences identified between polymer sub-diffusion and fractional Fokker-Planck models.

Results constrain the form of effective dispersion equations for such processes.

Abstract

In a very long Gaussian polymer on time scales shorter that the maximal relaxation time, the mean squared distance travelled by a tagged monomer grows as ~t^{1/2}. We analyze such sub-diffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the sub-diffusion described by the fractional Fokker-Planck equation. In particular, we show that the mean absorption time of diffuser between two absorbing boundaries is finite. Our results restrict the form of the effective dispersion equation that may describe such sub-diffusive processes.