article · 18/12/2012
Spatial log-periodic oscillations of first-passage observables in fractals
Résumé
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
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Akkermans, E., Benichou, O., Dunne, G.-V., Teplyaev, A., & Voituriez, R. (2012). Spatial log-periodic oscillations of first-passage observables in fractals. PHYSICAL REVIEW E, 86(6, 1). https://doi.org/10.1103/PhysRevE.86.061125@article{Akkermans2012_239,
author = {Akkermans, Eric and Benichou, Olivier and Dunne, Gerald V. and Teplyaev, Alexander and Voituriez, Raphael},
year = {2012},
month = {12},
title = {Spatial log-periodic oscillations of first-passage observables in fractals},
journal = {PHYSICAL REVIEW E},
volume = {86},
number = {6, 1},
abstract = {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},
url = {http://www.dx.doi.org/10.1103/PhysRevE.86.061125},
doi = {10.1103/PhysRevE.86.061125},
issn = {1539-3755},
}TY - JOUR
AU - Akkermans, Eric
AU - Benichou, Olivier
AU - Dunne, Gerald V.
AU - Teplyaev, Alexander
AU - Voituriez, Raphael
PY - 2012
DA - 2012/12/18
TI - Spatial log-periodic oscillations of first-passage observables in fractals
JO - PHYSICAL REVIEW E
VL - 86
IS - 6, 1
SN - 1539-3755
AB - 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
DO - 10.1103/PhysRevE.86.061125
UR - http://www.dx.doi.org/10.1103/PhysRevE.86.061125
ER -