PMID: 22587136May 17, 2012Paper

Critical condition of the water-retention model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Seung Ki Baek, Beom Jun Kim

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.

References

Dec 13, 1991·Science·H FrauenfelderP G Wolynes
Jul 27, 1987·Physical Review Letters·P BakK Wiesenfeld
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Don R BakerH Eugene Stanley
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·John A Quintanilla, Robert M Ziff
Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Robert M Ziff, Hang Gu
Mar 10, 2012·Physical Review Letters·Craig L KnechtRobert M Ziff

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Citations

Apr 4, 2012·Scientific Reports·K J SchrenkH J Herrmann
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K J SchrenkH J Herrmann

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