Pattern Formation, External Fields and Fluctuations

Abstract

Since the nucleation of spatio-temporal patterns in nonequilibrium systems is usually associated with continuous symmetry breakings, their selection and stability properties may be strongly affected by fluctuations or small external fields. These effects are discussed in the framework of amplitude equations of the Ginzburg-Landau type. In particular, it is shown that the presence of fluctuations modify qualitatively the bifurcation diagram and suppress any true long range order in low dimensional systems.KeywordsHopf BifurcationRange OrderAdvection TermAmplitude EquationPhase FluctuationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.