Estudo da formação e seleção de padrões na equação de Swift-Hohenberg

Abstract

We study numerically the pattern selection process in the Swift-Hohenberg equation with periodic boundary conditions. Two approaches were used for analyzing the emergence of the pattern: counting defects as a function of time and the determination ofthe dominant mode in Fourier space selected by the system, starting from diverse initial conditions. We and that the region of stability for patterns is limited by a secondary instability (the Eckhaus instability). The number of defects decays as a power-law with time. Although pairwise annihilation of defects should in principal generate power-law decay, this mechanism does not appear to apply in the present case. We seek, as well, to control the pattern through a feedback scheme, to selectively stabilize a mode different from the one with the highest growth rate.Keywords: convection, patterns, hydrodynamic instability