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.

Subject headings

NATURVETENSKAP  -- Fysik -- Den kondenserade materiens fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Condensed Matter Physics (hsv//eng)

Publication and Content Type

ref (subject category)

art (subject category)