Zhoujian Cao

Turbulence control with local pacing and its implication in cardiac defibrillation.

In this review article, we describe turbulence control in excitable systems by using a local periodic pacing method. The controllability conditions of turbulence suppression and the mechanisms underlying these conditions are analyzed. The local pacing method is applied to control Winfree turbulence (WT) and defect turbulence (DT) induced by spiral-wave breakup. It is shown that WT can always be suppressed by local pacing if the pacing amplitude and frequency are properly chosen. On the other hand, the pacing method can achieve suppression of DT induced by instabilities associated with the motions of spiral tips while failing to suppress DT induced by the instabilities of wave propagation far from tips. In the latter case, an auxiliary method of applying gradient field is suggested to improve the control effects. The implication of this local pacing method to realistic cardiac defibrillation is addressed.

Control of defect-mediated turbulence in the complex Ginzburg–Landau equation via ordered waves

Here, we study the local control of defect-mediated turbulence or spiral turbulence via ordered waves in the two- (2D) and three-dimensional (3D) complex Ginzburg–Landau equation (CGLE) systems. Depending on the local oscillating frequency resulting from the external periodic injection or the localized inhomogeneity, either spiral waves or target waves could be generated and they may successfully suppress the turbulent waves in the CGLE systems. Theoretical analysis combined with numerical analysis is given to reveal the underlying mechanism.

Negative refraction in nonlinear wave systems

Scientists have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line, has been predicted and realized in the context of linear optics in the presence of both right- and left-handed materials. In this work, we reveal, by theoretical prediction and numerical verification, negative refraction in nonlinear oscillatory systems. We demonstrate that unlike what happens in linear optics, negative refraction of nonlinear waves does not depend on the presence of the special left-handed material, but depends on suitable physical condition. Namely, this phenomenon can be observed in wide range of oscillatory media under the Hopf bifurcation condition. The complex Ginzburg-Landau equation and a chemical reaction-diffusion model are used to demonstrate the feasibility of this nonlinear negative refraction behavior in practice.

NEGATIVE PHASE VELOCITY IN NONLINEAR OSCILLATORY SYSTEMS — MECHANISM AND PARAMETER DISTRIBUTIONS

Waves propagating inwardly to the wave source are called antiwaves which have negative phase velocity. In this paper the phenomenon of negative phase velocity in oscillatory systems is studied on the basis of periodically paced complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture on the negative phase velocity of these pacing induced waves. This picture tells us that the competition between the frequency

Suppress Winfree turbulence by local forcing excitable systems.

omega_{out}

Removal of a pinned spiral by generating target waves with a localized stimulus.

of the pacing induced waves with the natural frequency

Suppression of Winfree turbulence under weak spatiotemporal perturbation

omega_{0}

Controlling turbulence in excitable media by applying boundary periodic pacing and gradient force

of the oscillatory medium is the key point responsible for the emergence of negative phase velocity and the corresponding antiwaves.

The effect of mechanical deformation on spiral turbulence

omega_{out}omega_{0}>0

Exact statistics of three-hard-disk system in two-dimensional space

and