"Plate tectonics" is art observed fact and most models of earthquake incorporate it through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to reproduce the well known Gutenberg-Richter type power law in the (released) energy distribution of earthquakes. During a sticking period. the elastic energy gets stored at the contact area of the surfaces and is released when a slip occurs. Therefore, the extent of the contact area between two surfaces plays an important role in the earthquake dynamics and the power law in energy distribution might imply a similar law for the contact area distribution. Since fractured surfaces are fractals and tectonic plate-earth's crust interfaces can be considered to have fractal nature, we study here the contact area distribution between two fractal surfaces. We consider the overlap set (m) of two self-similar fractals, characterized by the same fractal dimensions (d(f)), and look for their distribution P(m). We have studied numerically the specific cases of both regular and random Cantor sets (in the embedding dimension d = 1), gaskets and percolation fractals (in d = 2). We find that in all the cases the distributions show all universal finite size (L) scaling behavior P'(m') = (LP)-P-alpha(m, L); m' = mL(-alpha), where alpha = 2(d(f) - d). The P(m), and consequently the scaled distribution P'(m), have got a power law decay with m (with decay exponent equal to d) for both regular and random Cantor sets and also for gaskets. For percolation clusters, P(m) (and hence P'(m')) have a Gaussian variation with m. [References: 15]
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