title: Retention capacity of random surfaces.
abstract: We introduce a "water retention" model for liquids captured on a random surface with open boundaries and investigate the model for both continuous and discrete surface heights 0,1,…,n-1 on a square lattice with a square boundary. The model is found to have several intriguing features, including a nonmonotonic dependence of the retention on the number of levels: for many n, the retention is counterintuitively greater than that of an (n+1)-level system. The behavior is explained using percolation theory, by mapping it to a 2-level system with variable probability. Results in one dimension are also found.
authors.affiliation: craigknecht03@gmail.com
authors.forename: Craig L
authors.initials: CL
authors.lastname: Knecht
authors.forename: Walter
authors.initials: W
authors.lastname: Trump
authors.forename: Daniel
authors.initials: D
authors.lastname: Ben-Avraham
authors.forename: Robert M
authors.initials: RM
authors.lastname: Ziff