Directed compact percolation near a damp wall: mean length and mean number of wall contacts

Key aspects of the cluster distribution in the case of directed, compact percolation near a damp wall are derived as functions of the bulk occupation probability p and the wall occupation probability pw. The mean length of finite clusters and mean number of contacts with the wall are derived exactly, and we find that both results involve elliptic integrals and further multiple sum functions of two variables. Despite the added complication of these multiple sum functions, our analysis shows that the critical behaviour is similar to the dry wall case where these functions do not appear. We derive the critical amplitudes as a function of pw. PACS numbers: 05.50.+q, 0.5.70.fh, 64.60.ah (Some figures may appear in colour only in the online journal)