Abstract
AbstractWe study diffusion of Brownian particles on random fractal structures, self‐avoiding random walks and percolation clusters at criticality, which serve as model systems for polymers in a good solvent and random two‐component mixtures, respectively. Using numerical simulations and scaling arguments we find that the distribution function P(r, t) of the particles is a stretched Gaussian and scales as log[P(r, t)/P(r, 0)] ∼ —[r/R(t)]u, where R(t) ∼t1/dw is the root‐mean‐square displacement, u = dw/(dw‐1), and dw = 2df for self‐avoiding walks and dw = 3df/2 for percolation; df is the fractal dimension of the structure. In the presence of an external constant bias field, diffusion is drastically reduced and R(t) ∼ logt evolves logarithmically in time, in exactly the same way in both fractal structures.
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