Spatial log-periodic oscillations of first-passage observables in fractals.
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 an 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.
Department of Physics, Technion Israel Institute of Technology, Haifa 32000, Israel.
Eric
E
Akkermans
Olivier
O
Benichou
Gerald V
GV
Dunne
Alexander
A
Teplyaev
Raphael
R
Voituriez