Universality in edge-source diffusion dynamics.
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)2pi/(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.
Mortensen
Niels Asger
NA
MIC, Department of Micro and Nanotechnology, NanoDTU, Technical University of Denmark, Building 345 east, DK-2800 Kongens Lyngby, Denmark.
Okkels
Fridolin
F
Bruus
Henrik
H