Directed compact percolation near a damp wall with biased growth

Abstract

The model of directed compact percolation near a damp wall is generalized to allow for a bias in the growth of a cluster, either towards or away from the wall. The percolation probability for clusters beginning with seed width m, any distance from the wall, is derived exactly by solving the associated recurrences. It is found that the general biased case near a damp wall leads to a critical exponent ß=1, in line with the dry biased case, which differs from the unbiased damp/dry exponent ß=2. © 2012 IOP Publishing Ltd and SISSA Medialab srl.