DYNAMICS OF ONE-DIMENSIONAL INTERFACES - AN EXPERIMENTALISTS VIEW

Following the lead provided by a liquid-crystal directional ordering experiment, this article presents the current state of the art in dynamical bifurcations for one spatial dimension, or, in other words, various steps in the route to spatio-temporal chaos. After a presentation of the principles of marginal stability analysis, the specific case of the Mullins-Sekerka instability arising in directional solidification is thoroughly studied, as well as its extensions to more general analysis of instabilities. The bifurcations occurring in the liquid-crystal experiment, which can be classified according to symmetry considerations, are systematically presented. The parity-broken states-travelling waves and solitary modes-are shown to be especially important; they are generic bifurcations also recovered in other one-dimensional interface experiments detailed here, namely directional solidification of plastic crystals and eutectic mixtures, directional viscous fingering and Taylor-Dean flows.