Retention capacity of random surfaces
Disordered Systems and Neural Networks
2012-02-01 v3
Abstract
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.
Cite
@article{arxiv.1110.6166,
title = {Retention capacity of random surfaces},
author = {Craig L. Knecht and Walter Trump and Daniel ben-Avraham and Robert M. Ziff},
journal= {arXiv preprint arXiv:1110.6166},
year = {2012}
}
Comments
5 pages