He Kai-Fen

Suppressing Spatiotemporal Chaos via Non-feedback Pinning Method

The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is suppressed by the non-feedback pinning method. By adding additive external noise to the controlled state, we find that the deviation from the target spacetime pattern increases in a power law with noise intensity. The possible controlling mechanism is discussed.

Dust-Acoustic Solitons in Dusty Plasma with Two-Temperature Ions

Dust-acoustic solitons in dusty plasmas with two-temperature isothermal ions are investigated by considering an effect of self-consistent dust-charge variation. Employing the reductive perturbation technique we derived dust-acoustic solitons. It is found that both rarefactive and compressive solitons exist and the approximate similarity law which holds in dust-charge-fluctuation plasma system with one-temperature ion does not survive in the present studied dusty plasma with two-temperature isothermal ions.

Nonlinear localized structure in dusty plasma

The nonlinear effect of ponderomotive force of high-frequency ion motion on the low-frequency motion of ions coupling with the dust density fluctuation is investigated. The nonlinear localized structure described by Zakharov equations and nonlinear Schrodinger equation in dusty plasma are obtained. Envelope solitons for high-frequency ion motion and the dust density cavitons are also obtained and discussed.

Hopf Bifurcation in a Nonlinear Wave System

Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point. It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for further exploration of the routes to turbulence.

Dust-Acoustic Waves in Strongly Coupled Dusty Plasmas Containing Variable-Charge Impurities

A relatively self-consistent theory of dust-acoustic waves in the strongly coupled dusty plasmas containing variable-charge impurities is given. Relevant physical processes such as dust elastic relaxation and dust charge relaxation are taken into account. It is shown that the negative dispersion of dust-acoustic waves due to the strong correlation of dusts is enhanced in the presence of dust-neutral collisions.

Time-Correlation Function for Periodically-Forced Nonlinear Stochastic System*

The equilibrium time-correlation function for a general cosine-forced stochastic system are calculated respectively by the perturbation theory and the linear response theory. The results obtained by the two theories are basically identical. By calculation we find that it has two terms. One is the original time-correlation function (in the case when the external signal does not exist). The other is caused by the perturbing external signal. The two terms have the same relaxation time, and the latter has oscillator behavior.

Phase Synchronization as a Mechanism of Controlling Spatiotemporal Chaos via External Periodic Signal

We find that phase synchronization (PS) is a mechanism in which the spatiotemporal chaos (STC) can be suppressed to a spatially regular (SR) state by applying an external periodic signal in a one-dimensional driven drift-wave system. In the driving wave coordinate, the nonlinear system can be transformed to a set of coupled oscillators moving in a periodic potential. In this multi-dimensional system, the internal modes are slaved one by one through PS by the control signal. Two types of responses of the internal modes to the external periodic signal are observed. For some modes, the stabilization is through frequency-locking; while for the other modes, a special kind of PS without frequency-locking, namely multi-looping PS, is developed.

Quantum Poincaré Section of a Two-Dimensional Hamiltonian in a Coherent State Representation

We study the quantum behaviour of a quasi-integrable Hamiltonian. The unperturbed Hamiltonian displays degeneracies of energy levels, which become avoided crossings under a nonintegrable perturbation. In this two-dimensional system, the quantum Poincare section plot is constructed in the coherent state representation with the restriction that the centres of the wavepackets are confined at the classical surface of constant energy. It is found that the quantum Poincare section plot obtained in this way provides an evident counterpart of the classical system.

Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields

We investigate charged particle motion in temporal chaotic and spatiotemporal chaotic fields. In its steady wave frame a few key modes of the solution of the driven/damped nonlinear wave equation are used as the field. It is found that in the spatiotemporal chaotic field the particle drifts relative to the steady wave, in contrast to that in the temporal chaotic field where the particle motion is localized in a trough of the wave field. The result is of significance for understanding stochastic acceleration of particles.

Suppression of Instability in Strongly Coupled Dusty Plasmas with Ion Flow

The instability of low-frequency longitudinal modes in strongly coupled dusty plasmas with an ion flow is investigated. The dust charging relaxation is taken into account. It is found that when the ion flow is strong enough, the suppression, even disappearance, of instability can occur. Similar to that of the real frequency of waves, the imaginary part of waves also exhibits a transition, which arises from the sensitive dependences on the system parameters and their competition.