Diffusion in a stirred, percolating system

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Abstract
The problem of stirred percolation, which has been proposed to model various systems with annealed disorder (including globular-phase microemulsions), is formulated as a continuous-time random walk. Transport quantities, such as the dc diffusion constant, depend both on the statistics of the instantaneous clusters near the percolation threshold and on their rearrangement times. The scaling of these rearrangement times is discussed, and it is shown that both small clusters and large ones affect the scaling behavior of various physical quantities. Qualitatively, the diffusion process resembles a Levy flight, with the duration of large steps being shorter than that of small steps. For some range of parameters, the diffusion constant scales differently than it does in quenched percolation. The natural scaling variables, and therefore the predicted scaling behaviors, are found to differ from previous predictions.