Generation Mechanism of a Localized Target Pattern in Electrohydrodynamic Convection

A localized target pattern is observed in the grid pattern of the electro-hydrodynamic convection of a nematic liquid crystal. The target pattern is created by a phase instability through the coupling between the oscillation of an underlying grid and the deformation of the grid. By determining the coefficients of phase equations derived from coupled complex Ginzburg-Landau equations, we confirm that the equations describe the instability in the system. Moreover we found that the critical voltage for Hopf bifurcation depends on the grid wavenumber. This effect explains the localization of target.