Concentration gradient approach to continuum percolation in two dimensions

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Abstract
The author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration. Fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice. This is in agreement with the universality of critical exponents of percolation. The concentration gradient approach permits a precise calculation of the percolation threshold, corresponding to a critical area fraction of 0.6766+or-0.0005. He has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes. The fractal dimension of this 'accessible' perimeter is found to decrease abruptly as a function of the radius of invading discs, from 1.75+or-0.02 to 1.35+or-0.02.