Defects and Transition to Disorder in Space-Time Patterns of Non-Linear Waves
The traveling-wave convection found in a liquid crystal gives an example of nonlinear waves. The basic state is a uniform progressive wave which is a perfectly ordered structure in space-time. We present an experimental study of some elementary mechanisms that trigger the nucleation of defects in waves and we show that these defects mediate a transition to a chaotic state. It is found that a homogeneous progressive wave can become unstable against local perturbations of the phase which generally have a shock structure. The shocks give rise to topological singularities that are defects of the space-time ordering. It is shown that the structure and the role of these defects in the evolution to a space-time disordering are reminiscent of that of the dislocations and the grain boundaries in stationary convective structures. Some numerical simulations of defects nucleation by use of a Landau-Ginzburg equation, are also presented.
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