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≊${\mathit{n}}^{\mathrm{\beta }}$, where n is the particle number removed from metal) is given by β=${\mathit{D}}_{\mathit{n}}$(1) where ${\mathit{D}}_{\mathit{n}}$(1) is the information dimension. It is also shown that the scaling exponent β is related to the maximum growth probability ${\mathit{p}}_{\max }$ at the edge of the corrosion pit and approximately given by β=1-${\mathit{D}}_{\mathit{n}}$(∞).