Critical condition of the water-retention model

We study how much water can be retained without leaking through boundarieswhen each unit square of a two-dimensional lattice is randomly assigned a blockof 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 whichthe system retains a macroscopic volume of water.We locate the critical points and verify that the criticalitybelongs 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 areabelow the resulting water level is given by the percolation threshold.This provides a universal upper bound ofareas that can be covered by water in a random landscape.

Kim, Beom JunDepartment of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea (författare)
Umeå universitetInstitutionen för fysik (creator_code:org_t)

Ingår i:Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: American Physical Society85:3, s. 032103-1539-37551550-2376

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