| Abstract
| - The diffusion-limited reaction rate isdetermined on an approximately self-affine corrugated (random)surfacefractal. We obtain the exact result for the low roughness and theasymptotic results (in three time regions)for the arbitrary and large roughness surfaces. These results showthe anomalous time dependence for themean flux and the mean excess flux for the large and small roughnesssurfaces, respectively. The intermediatetime behavior of the reaction flux for the small roughness interfacehas the form 〈J〉 ∼t-1/2 + constt-3/2+H,but for the large roughness interfaces it has same form as predictedearlier, 〈J〉 ∼t-1+H/2,where H is Hurst'sexponent. This nonuniversality and dependence of intermediate timebehavior on the strength of fractality ofthe interface is not conceived by earlier works. We also show thelocalization of the active zones in thepresence of roughness. Finally, these results unravel theconnection between the total reaction flux and thecrossover times to the roughness characteristics like fractaldimension, lower and upper fractal cutoff lengths,and the amplitude of the fluctuations (strength) of thefractal.
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