Mortensen Niels Asger, Okkels Fridolin, Bruus Henrik
MIC, Department of Micro and Nanotechnology, NanoDTU, Technical University of Denmark, Building 345 east, DK-2800 Kongens Lyngby, Denmark.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 1):012101. doi: 10.1103/PhysRevE.73.012101. Epub 2006 Jan 24.
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.
我们表明，在边缘源扩散动力学中，积分浓度N(t)与一个特征时间尺度tau=(A/P)2π/(4D)存在普遍依赖关系，其中D是扩散常数，而A和P分别是区域的横截面积和周长。对于短时间动力学，我们发现一种普遍的平方根渐近依赖关系N(t)=N0√(t/tau)，而在长时间动力学中，N(t)在N0处呈指数饱和。指数饱和是一个普遍特征，而相关系数对几何形状的依赖较弱。
