Multifractality of growth probability distribution in diffusion-limited-corrosion pit

The multifractal structure of the growth probability distribution on the perimeter of a pit in the diffusion-limited pitting corrosion is derived by making use of the Monte Carlo estimation of the hitting probabilities by successive launching of a large number of random walkers. The multifractal spectrum {α}-f({α}) is determined, and compared with that of the diffusion-limited aggregation. It is found that the scaling exponent {β} of width w of the corrosion pit (w{}n^β, where n is the particle number removed from metal) is given by {β}=Dₙ(1) where Dₙ(1) is the information dimension. It is also shown that the scaling exponent {β} is related to the maximum growth probability pₘₐₓ at the edge of the corrosion pit and approximately given by {β}=1-Dₙ({∞}).