Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities $p<1$ of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on $p$ and with diffusion exponents that depend on the dimensions of matrix $\left(E\right)$ and fractal $\left(D_F\right)$ as $\nu =1/(2+D_F-E)$. This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for $p\lesssim {10}^{-3}$ and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.

Close

PrevNext

View figure in article

• Anomalous diffusion
• Diffusion
• Domains
• Random walks
• Rocks
• Composite materials
• Fractals
• Lattice models in statistical physics
• Porous materials
• Cellular automata
• Fractal dimension characterization
• Monte Carlo methods
• Scaling methods