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)(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)=N(0)root t/tau while in the long-time dynamics N(t) saturates exponentially at N-0. The exponential saturation is a general feature while the associated coefficients are weakly geometry dependent.