Numerical investigation of a fractional diffusion model on circular comb-inward structure. (February 2020) - Liu, Chunyan; Fan, Yu; Lin, Ping
Abstract: In this paper, the diffusion dynamics of particles on a circular comb-inward structure with different radial and tangential mobilities are studied. The Scott-Blair time-fractional memory model is exploited to incorporate the trapping process in the diffusion. A new formulation of particle flux is proposed for which the numerical discretization is straightforward. The numerical scheme is based on the second-order L 2 − 1 σ formula for time stepping and uses the finite difference method for spatial approximations. The influences of involved parameters on the distribution of particles and the mean-square displacement (MSD) are investigated in detail. According to the model prediction, the diffusion of particles on the ring decreases with the smaller values of the fractional order α . Results also indicate that the radial and tangential mobilities exhibit the opposite effects on the MSD of particles.