Scaling Theory of Instability, Nonlinear Fluctuation and Formation of Macroscopic Structure

Abstract

The general scheme of the scaling theory of transient phenomena near the instability point is reviewed. The essence of this theory is to evaluate asymptotically nonlinear fluctuations and to study onset of macroscopic structure or order for large system size Ω and for large time. The so-called scaling regime is the most interesting second intermediate time region, in which there occurs fluctuation enhancement and its enhanced fluctuation changes into macroscopic order or structure in unstable systems. Applications of this scaling theory to transient laser radiation and chemical reaction (for the Brusselator) are presented.KeywordsTransient PhenomenonInstability PointInitial RegimeMacroscopic StructureScaling TheoryThese 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.