Abstract
We study the continuum percolation in systems composed of overlapping objects of two different sizes. We show that when treated as a function of the volumetric fraction f as opposed to the concentration x, the percolation threshold exhibits the symmetry η c ( f, r)= η c (1− f, r) where r is the ratio of the volumes of the objects. Knowledge of this symmetry has the following benefits: (i) the position of the maximum of the percolation threshold is then known to be at exactly f=1/2 for any r and (ii) full knowledge of the percolation threshold is obtained by performing simulations only for f∈[0, 1 2 ] or f∈[ 1 2 ,1] , whichever is computationally easier.
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