Journal
PHYSICAL REVIEW E
Volume 73, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.73.021104
Keywords
-
Categories
Ask authors/readers for more resources
Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRWs) with transition probability densities showing space- and/or time-diverging moments were developed to account for anomalous behaviors. A broad class of CTRWs was shown to correspond, on the macroscopic scale, to advection-diffusion equations involving derivatives of noninteger order. In particular, CTRWs with Levy distribution of jumps and finite mean waiting time lead to a space-fractional equation that accounts for superdiffusion and involves a nonlocal integral-differential operator. Within this framework, we analyze the evolution of particles performing symmetric Levy flights with respect to a fluid moving at uniform speed v. The particles are restricted to a semi-infinite domain limited by a reflective barrier. We show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator. Thus, the macroscopic space-fractional advection-diffusion equation obtained is different from that in an infinite medium.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available