Retention capacity of random surfaces

TL;DR

This paper introduces a water retention model on random surfaces, revealing complex behaviors like non-monotonic retention dependence on surface levels, explained through percolation theory, with results applicable in both 2D and 1D cases.

Contribution

It presents a novel water retention model on random surfaces, analyzing its properties and explaining non-intuitive behaviors using percolation theory.

Findings

Retention peaks at certain levels due to percolation effects

Counterintuitive higher retention in systems with more levels

Analytical results in 1D extend the understanding of the model

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.