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 Lévy-like process enriches this transport phenomenon. It is shown that an inhomogeneous convection flow is a mechanism for the realization of the Lévy-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.
Fractional transport of particles on a comb structure in the presence of an inhomogeneous convection flow is studied [Baskin and Iomin, Phys. Rev. Lett. 93, 120603 (2004)]. The large scale asymptotics is considered. It is shown that a contaminant spreads superdiffusively in the direction opposite to the convection flow. Conditions for the realization of this effect are discussed in detail.
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical
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