He Ya-Feng

Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback

The controllable transition between the Turing and antispiral patterns is studied by using time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as perturbation and analyze the effect of the time delay on the Turing and Hopf instabilities near the Turing-Hopf codimension-two phase space. Numerical simulations show the transition between the Turing patterns (hexagon, stripe, and honeycomb), the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.

Mode transition in homogenous dielectric barrier discharge in argon at atmospheric pressure

The influence of driving frequency on the discharge regime of a homogenous dielectric barrier discharge in argon at atmospheric pressure is studied through a one-dimensional self-consistent fluid model. The simulation results show that the discharge exhibits five notable discharge modes, namely the Townsend mode, stable glow mode, chaotic mode, asymmetric glow, and multiple period glow mode in a broad frequency range. The transition mechanisms of these modes should be attributed to the competition between the applied voltage and the memory voltage induced by the surface charges.

Experimental Observation of Travelling Hexagon Patterns in Dielectric Barrier Discharge

Travelling hexagon patterns have been observed in dielectric barrier discharge in an air-argon mixture. The phase diagram of hexagon pattern appearance as functions of applied voltage and air concentration is given. The spatial frequency of hexagon pattern increases with increasing applied voltage and air concentration. The current waveforms of hexagon pattern also vary with the air concentration. The drift velocity of travelling hexagon pattern changes from 4 mm/s to 18 mm/s.

Superlattice Patterns in Coupled Turing Systems

In this paper, superlattice patterns have been investigated by using a two linearly coupled Brusselator model. It is found that superlattice patterns can only be induced in the sub-system with the short wavelength. Three different coupling methods have been used in order to investigate the mode interaction between the two Turing modes. It is proved in the simulations that interaction between activators in the two sub-systems leads to spontaneous formation of black eye pattern and/or white eye patterns while interaction between inhibitors leads to spontaneous formation of super-hexagonal pattern. It is also demonstrated that the same symmetries of the two modes and suitable wavelength ratio of the two modes should also be satisfied to form superlattice patterns.

Simulation Study on the Self-Sustained Oscillations in DC Driven Glow Discharges at Atmospheric Pressure Under Different Gas Gaps

In this paper, a one-dimensional plasma fluid model is employed to study the self-sustained oscillations in DC-driven helium glow discharges at atmospheric pressure under different gas gaps. Our simulation results indicate that a harmonic current oscillation with tiny amplitude always occur at the onset of instability and transits into a relaxation one as the conductivity of the semiconductor is decreased. It is found that the dynamics of the oscillations are dependent on the gas gaps. The discharge can only exhibit a simple oscillation with unique amplitude and frequency at smaller gas gaps ( 2 mm). The discharge modes in these current oscillations have also been analyzed.

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system*

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.

Dynamics of Front Driven by Convection Field in Bistable Media

The front dynamics driven by a convection field in a model of FitzHugh—Nagumo type is studied both analytically and numerically. Saddle-node bifurcation induced by the convection field is found by using a singular perturbation analysis of front solutions. Convection field accelerates the Bloch front propagating opposite the direction of convection field, but inhibits the Bloch front propagating along the direction of convection field. In addition convection field drives Ising front to travel opposite the direction of convection field.