Year: 2006
Type: article
Abstract: We show that in edge-source diffusion dynamics the integrated concentration $N(t)$ has a universal dependence with a characteristic time scale $\ensuremath{\tau}=(\mathcal{A}∕\mathcal{P}{)}^{2}\ensuremath{\pi}∕(4D)$, where $D$ is the diffusion constant while $\mathcal{A}$ and $\mathcal{P}$ are the cross-sectional area and perimeter of the domain, respectively. For the short-time dynamics we find a universal square-root asymptotic dependence $N(t)={N}_{0}\sqrt{t∕\ensuremath{\tau}}$ 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.
Source: Physical Review E
Institution: Technical University of Denmark
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2030179599