A 1-d Ising model for ripple formation
Disordered Systems and Neural Networks
2007-05-23 v1
Abstract
A 1-d Ising model is shown to reproduce qualitatively the dynamics of ripple formation. Saltation effect is imposed using a Kawasaki dynamics and a pair interaction over some distance l. Within this model, the ripple state turns out to be metastable in agreement with cellular automata simulations as well as recent under water experiments. A dynamical phase diagram is obtained. A mean-field solution of the problem is given in terms of the ripple size. A mapping is then performed onto a 2-dimensional l x infinity static problem.
Cite
@article{arxiv.cond-mat/0205311,
title = {A 1-d Ising model for ripple formation},
author = {Nicolas Vandewalle and Serge Galam},
journal= {arXiv preprint arXiv:cond-mat/0205311},
year = {2007}
}
Comments
12 pages, 6 figures