Subdiffusion–Superdiffusion Random-Field Transition

Abstract

A contaminant spreading affected by a random field at boundaries in the comb geometry is considered. The physical effect of the random boundary conditions results in increasing a transport exponent such that the mean squared displacement increases with time from t12 to t12+5α/2 for real 0≤α≤1. This stochastic acceleration due to these space-time-dependent boundary conditions leads to a transition from subdiffusion to superdiffusion. Experimentally, it can be realized by controlling the boundary conditions of 2D diffusion in the comb geometry.

Keywords

• comb model
• Edwards–Wilkinson equation
• stochastic Fokker–Planck equation
• fractional Edwards–Wilkinson equation
• stochastic acceleration