ILLUMINATION - A NEW METHOD FOR STUDYING 3D PERCOLATION FRONTS IN A CONCENTRATION GRADIENT

A new method of studying percolation fronts is introduced in situations where the concentration is not constant (gradient percolation approach): it consists in an efficient way of determining subsets of the percolation cluster which are exactly at the percolation threshold. The method is applied to both lattice and continuum percolation in order to determine the percolation threshold in 3D more accurately. Two variations of this method, illumination and projection, seem to give a similar scaling behaviour at low gradients for the cubic lattice case, leading to a new estimate for the percolation threshold: p(c) = 0.311 73 +/- 0.000 07. For continuum percolation of overlapping spheres, the new estimate for the critical volume fraction is 0.291 +/- 0.002, and the value of the critical exponent alpha(sigma) for the width of the front scaled with the concentration gradient is very close to the one for the lattice case.