  For transport processes in geometrically restricted domains, the mean
first-passage time (MFPT) admits a general scaling dependence on space
parameters for diffusion, anomalous diffusion, and diffusion in disordered or
fractal media. For transport in self-similar fractal structures, we obtain a
new expression for the source-target distance dependence of the MFPT that
exhibits both the leading power law behavior, depending on the Hausdorff and
spectral dimension of the fractal, as well as small log periodic oscillations
that are a clear and definitive signal of the underlying fractal structure. We
also present refined numerical results for the Sierpinski gasket that confirm
this oscillatory behavior.
