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Ultrafine smoke particles stick together to form chain-like aggregates. It is found that the particle density has long-range correlations of the same form in iron, zinc of silicon dioxide aggregates. The correlation data suggest a power-law spatial dependence giving a Hausdorff dimension between 1.7 and 1.9. The authors discuss the consistency of these results with a model based on percolation. They also compare their results with a random-walk model, which has a nominal Hausdorff dimension of 2.
Forrest et al. (1979) studied this question.