Craig L. Knecht, Walter Trump, Daniel ben-Avraham, Robert M. Ziff
We introduce a "water retention" model for liquids captured on a random
surface with open boundaries, and investigate it for both continuous and
discrete surface heights 0, 1, ... n-1, on a square lattice with a square
boundary. The model is found to have several intriguing features, including a
non-monotonic dependence of the retention on the number of levels in the
discrete case: for many n, the retention is counterintuitively greater than
that of an n+1-level system. The behavior is explained using percolation
theory, by mapping it to a 2-level system with variable probability. Results in
1-dimension are also found.
View original:
http://arxiv.org/abs/1110.6166
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