| Popis: |
There exist disordered media where contaminant dispersion is conveniently described by Levy statistics. The case of enhanced diffusion corresponds to small scale motions, in the form of Continuous Time Random Walks with transition probability densities presenting spatial diverging moments. Such CTRWs in infinite media were shown to correspond, on the macroscopic scale, to diffusion equations involving Riesz-Feller derivatives of non-integer order, which are non-local w.r.t. space. For this reason, introducing boundary conditions sometimes results in modifying the large-scale model. We are studying here the diffusive limit of CTRWs, generalizing symmetric Levy flights in a bounded medium, limited by two reflective barriers. The thus obtained space-fractional diffusion equations differ from the infinite domain case. |
