title: Critical condition of the water-retention model.
abstract: We study how much water can be retained without leaking through boundaries when each unit square of a two-dimensional lattice is randomly assigned a block of unit bottom area but with different heights from zero to n-1. As more blocks are put into the system, there exists a phase transition beyond which the system retains a macroscopic volume of water. We locate the critical points and verify that the criticality belongs to the two-dimensional percolation universality class. If the height distribution can be approximated as continuous for large n, the system is always close to a critical point and the fraction of the area below the resulting water level is given by the percolation threshold. This provides a universal upper bound of areas that can be covered by water in a random landscape.
authors.affiliation: Integrated Science Laboratory, Umeå University, Umeå, Sweden.
authors.forename: Seung Ki
authors.initials: SK
authors.lastname: Baek
authors.forename: Beom Jun
authors.initials: BJ
authors.lastname: Kim
mesh_terms: D000042:Absorption; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D014867:Water / Q000737:chemistry*
chemical_list: D014867:Water