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Bulletin of the Korean Chemical Society (BKCS)

ISSN 0253-2964(Print)
ISSN 1229-5949(Online)
Volume 26, Number 11
BKCSDE 26(11)
November 20, 2005 

Fractional Diffusion Equation Approach to the Anomalous Diffusion on Fractal Lattices
Dann Huh, Jinuk Lee, Sangyoub Lee*
Fractional diffusion equation, Continuous time random walk, Dispersive diffusion, Sierpinski gasket, Percolation cluster
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 ψ (t) ~ t -(α+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 2α /dw, where dw 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.
1723 - 1727
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