Spatial log-periodic oscillations of first-passage observables in fractals

E. Akkermans , O. Benichou , G.V. Dunne , A. Teplyaev , R. Voituriez

Bibtex , URL
Published 18 Dec. 2012
DOI: 10.1103/PhysRevE.86.061125
ISSN: 1539-3755


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. DOI: 10.1103/PhysRevE.86.061125

Cette publication est associée à :

Dynamique stochastique des systèmes réactifs et vivants