Critical condition of the water-retention model
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 85, no 3, 032103- p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
American Physical Society , 2012. Vol. 85, no 3, 032103- p.
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:umu:diva-54259DOI: 10.1103/PhysRevE.85.032103ISI: 000302117900008OAI: oai:DiVA.org:umu-54259DiVA: diva2:517215
FunderSwedish Research Council, 621-2008-4449