Fractional Diffusion Equation Approach to the Anomalous Diffusion on Fractal Lattices

Bulletin of the Korean chemical society

Sangyoub Lee¹  Dann Huh¹  Jinuk Lee¹ 

关键词: Fractional diffusion equation;    Continuous time random walk;    Dispersive diffusion;    Sierpinski gasket;    Percolation cluster;   

DOI  :  

学科分类：化学（综合）

来源: Korean Chemical Society

【 摘 要 】

A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as �? (t) ~ t ^-(�?+1), the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < r²(t)> ~ t ^{2�? /dw}, where d_w is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.

【 授权许可】

Unknown