On intrinsic properties of fractal lattices and percolation clusters

On intrinsic properties of fractal lattices and percolation clusters

2014 Certain properties of fractal lattices are independent of the Euclidean embedding. The implications of this invariance are discussed for various problems : the conductivity of percolation clusters, inequalities between intrinsic dimensions, and the diffusion coefficient in a flow through a porous medium. J. Physique Lett. 45 (1984) L-1071 L-1076 15 NOVEMBRE 1984, Classification Physics Abs...

Random walks on fractal structures and percolation clusters

Diffusion noise of fractal networks and percolation clusters.

Diffusion noise and Nyquist noise on fractal lattices and percolation clusters are discussed in the highand low-frequency limits. Diffusion noise can also be considered as a sort of "1/f noise. " Even for system sizes much larger than the correlation length, the fractal structure of the percolation clusters reveals itself at sufficiently high frequencies through the anomalous frequency dependen...

Fractal dimensions of confined clusters in two – dimensional directed percolation

The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic–like systems, is studied in two dimensions via Monte–Carlo simulations. With a free surface at y=±Cx k and a dynamical exponent z, the surface shape is a relevant perturbation when k<1/z and the fractal dimensions of the anisotropic clusters vary continuously with k. Analytic expressions ...

On surface properties of two-dimensional percolation clusters

The two-dimensional site percolation problem is studied by transfermatrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal invariance, allows a very precise determination of the surface decay-of-correlations exponent, ηs = 0.6664 ± 0.0008, consistent with the analytical value ηs = 2/...