Dinâmica da formação de padrões: precursores, morfologia e seleção de modos em um sistema perturbado

Abstract

In this work, an experimental study of a spatial-temporal pattern forming system, was performed and analyzed. The pattern generated in that system was subject to a deterministic perturbation. This controlled perturbation changes dynamically an important control parameter of the system and because of this many nontrivial effects arose in its pre and post-bifurcation branches. The system we studied, a one-dimensional hydrodynamic interface, can be monitored with great precision in the laboratory. Using image processing techniques we were able to capture the pattern dynamics in the presence of that perturbation. The data were treated with Fourier and statistical analysis which allowed us to obtain measurements of that uid-uid interface. In the prebifurcation branch,the effects of the perturbation were perceived as a critical amplication of the oscillations in the interface position. They present the same features of a precursor which is a kind of instability in a nonequilibrium system observed prior to a bifurcation. After the bifurcation, the imposed perturbation affected the evolution of pattern modes and itsefects persisted even when there was a saturation of mode amplitudes. Our observations also indicate that pattern morphology is associated with a wave vector selection process. We were able to make detailed measurement of pattern shape and its associated Fourier modes. They assured the detection of a crossover between two diferent regimes of the pattern evolution. This way, the interaction between time domain, consisting of precursor activities, and spatial domain, when a periodic pattern is present, was explored and it was responsible for the spatiotemporal effects observed in the system we have studied.