Numerical analysis on formation and transition of white-eye square superlattice patterns in dielectric barrier discharge system

Abstract

The mechanism of formation and transformation of white-eye square patterns in dielectric barrier discharge system is investigated numerically, using the two-layer Lengyel–Epstein model with asymmetric and symmetric coupling. When the scale of the simulation system [Formula: see text] is two to three times of pattern wavelength [Formula: see text], it is found that an obvious intermediate state with square distribution appears by adjusting the ratio of diffusion coefficients [Formula: see text]/[Formula: see text]. When it is coupled with a suitable short-wavelength Turing mode in the range of [Formula: see text] to [Formula: see text], a new spatial resonance structure can be formed in the short-wavelength mode subsystem, and the pattern evolves from a simple square pattern to a white-eye square pattern. Although the two coupling methods achieve the same results, the duration time of the white-eye square pattern in the symmetric coupling method is significantly longer than that in the asymmetric coupling method. Because the quadratic coefficient of the amplitude equation in the reaction–diffusion system is not zero, the simple square pattern of the long wavelength mode subsystem gradually transits into a stable hexagon pattern gradually. As a result, the white-eye pattern transits from a square to a hexagon.