Superdiffusion on a comb structure

We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of the Levy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Levy-like process. It leads to superdiffusion of particles on the comb structure. This superdiffusion is an enhanced one with an arbitrary large transport exponent, but all moments are finite. A frontier case of superdiffusion, where the transport exponent approaches infinity, is studied. The log-normal distribution with the exponentially fast superdiffusion is obtained for this case.