Universality in edge-source diffusion dynamics
Other Condensed Matter
2007-05-23 v2 Classical Physics
Abstract
We show that in edge-source diffusion dynamics the integrated concentration N(t) has a universal dependence with a characteristic time-scale tau=(A/P)^2 pi/(4D), where D is the diffusion constant while A and P are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence N(t)=N0 sqrt(t/tau) while in the long-time dynamics N(t) saturates exponentially at N0. The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.
Cite
@article{arxiv.cond-mat/0510627,
title = {Universality in edge-source diffusion dynamics},
author = {N. A. Mortensen and F. Okkels and H. Bruus},
journal= {arXiv preprint arXiv:cond-mat/0510627},
year = {2007}
}
Comments
4 pages including 4 figures. Minor changes. Accepted for PRE