ENHANCED DIFFUSION IN RANDOM VELOCITY-FIELDS

We study superlinear diffusion in a layered medium containing random velocity fields, where the mean-squared displacement grows as x2(t)t with >1 [S. Redner, Physica D 38, 287 (1989)]. For a two-dimensional system with preassigned random velocities in the longitudinal x direction and with diffusional motion in the transversal direction, we determine exactly the asymptotic behavior of the first three nontrivial moments M2m=x2m(t)/x2(t)m of the displacement. Furthermore, we succeed in relating the diffusional problem to the one-dimensional trapping problem. We then are in a position to analyze the scaling form of the propagator P(x,t)t-3/4f(x3/4), where the function f(z) obeys a complicated stretched exponential behavior. We also generalize the problem to transverse motion on fractals and ultrametric spaces that leads to values that interpolate between 1 and 2. We support our theoretical analytical results by simulation calculations. © 1990 The American Physical Society.