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I try to investigate the damage of the metal surface with box-counting method (input data is SEM surface images) - some surfaces give a convex multifractal spectrum [f(α(q))=α(q)*q-τ(q) versus α(q)] for a result - which is also widespread in the literature, but some other surface images form a concave multifractal spectrum. Multifractal spectrum of damaged metal surface

Not much information is available on this concave fractal spectrum - how could it be interpreted in physically?

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