We report on the first investigation of the triple-layer coupling pattern formation in a dielectric barrier discharge system. The pattern basically consists of one discharge subpattern ignited in the gas gap and two surface-charge subpatterns deposited on the dielectric surfaces. The coupling of the three subpatterns (layers) is presented by analyzing the time-resolved discharge sequence of a white-eye hexagonal super lattice pattern (WEHSP). A triple-layer coupling reaction-diffusion regime is also established to conduct simulations and the simulated WEHSP agrees well with the experiment. This paper will provide a deeper understanding for the layer coupling mechanism in pattern formation.
We study the interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet. By means of a reasonable assumption and a straightforward Darboux transformation one-and two-soliton solutions in a nonlinear spin-wave background are obtained analytically, and their properties are discussed in detail.In the background of a nonlinear spin wave the amplitude of the envelope soliton has the spatial and temporal period, and soliton can be trapped only in space. The amplitude and wave number of spin wave have the different contribution to the width, velocity, and the amplitude of soliton solutions, respectively. The envelope of solution hold the shape of soliton, and the amplitude of each envelope soliton keeps invariability before and after collision which shows the elastic collision of two envelope soliton in the background of a nonlinear spin wave.
The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.
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