Article,
Flow in porous media: The "backbone" fractal at the percolation threshold
Physical Review B, 29 (1): 522--524 (January 1984)
DOI: 10.1103/physrevb.29.522
Abstract
We show that for all Euclidean dimensions d ζ̃= d ̅ w - d ̅ f ; where L R ∼ξ ζ̃ is the effective resistance between two points separated by a distance comparable with the correlation length ξ; d ̅ f is the fractal dimension of the backbone; and d ̅ w is the fractal dimension of a random walk on the same backbone. We also find a relation between the backbone and the full percolation cluster; d ̅ w - d ̅ f = d w - d f . Thus the Alexander-Orbach conjecture ( d f / d w =2 / 3 for d > \~2) fails numerically for the backbone.
