Traveling time and traveling length in critical percolation clusters

We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time t(min) scales as t(min)similar to r(1.33), which is different from the scaling of the most probable traveling time, (t) over tilde similar to r(1.64). We also calculate the length of the path corresponding to the minimal traveling time and find l(min)similar to r(1.13) and that the most probable traveling length scales as (l) over tilde similar to r(1.21). We present the relevant distribution functions and scaling relations, [S1063-651X(99)02809-3].