On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid
Abstract
We model the behavior of a big (Brazil) nut in a medium of smaller nuts with a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice system. The polymer or `rod' can move up or down in an external negative field, occupying N horizontal lattice sites where the monomers cannot enter. The monomers (at most one per site) or `fluid particles' are moving symmetrically in the horizontal plane and asymmetrically in the vertical direction, also with a negative field. For a fixed position of the rod, this lattice fluid is in equilibrium with a vertical height profile reversible for the monomers' motion. Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically decouples from that of the monomers resulting in a reversible random walk for the rod around an average height proportional to log N.
Keywords
Cite
@article{arxiv.math/0001073,
title = {On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid},
author = {Pablo. A. Ferrari and Christian Maes and Laura Ramos and Frank Redig},
journal= {arXiv preprint arXiv:math/0001073},
year = {2011}
}
Comments
19 pages, 2 figures