Walking on fractals: diffusion and self-avoiding walks on percolation clusters

Abstract

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d=2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs.

21 pages

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• Fractals Meet Fractals: Self-Avoiding Random Walks on Percolation Clusters
• Equivalence of quenched and annealed averaging in models of disordered polymers
• Spreading processes in "post-epidemic" environments
• Self-Avoiding Walk on the square site-diluted Ising-correlated lattice
• Linear Polymers in Disordered Media - the shortest, the longest and the mean(est) SAW on percolation clusters
• Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
• Polymers in anisotropic environment with extended defects
• Theta-polymers in crowded media under the stretching force
• Optimization of multisite reactions in complex compartmentalized media
• Coagulation-flocculation process on a lattice: Monte Carlo simulations
• Spreading processes in "post-epidemic" environments. II. Safety patterns on scale-free networks