Abstract
We show that in edge-source diffusion dynamics the integrated concentration has a universal dependence with a characteristic time scale , where is the diffusion constant while and are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence while in the long-time dynamics saturates exponentially at . The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.
- Received 24 October 2005
DOI:https://doi.org/10.1103/PhysRevE.73.012101
©2006 American Physical Society