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A 1-d Ising model for ripple formation

Nicolas Vandewalle·Serge Galam
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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.

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Nicolas Vandewalle, Serge Galam. 2002-05-15. A 1-d Ising model for ripple formation. https://arxiv.org/abs/cond-mat/0205311

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