Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

Stability of Dust Acoustic Waves in Weakly Two—Dimensional Dust Plasma with Vortex—Like Ion Distribution

By considering the vortex-like ion distribution,we know that the nonlinear dust acoustic wave can be described by the modified Korteweg-de Vries equation.If there are high-order transverse perturbations in this system,the governing equation for this system is the modified Kadomtsev-Petviashvili equation.We also find that for this system under the transverse perturbation the one-dimensional solitary wave solution is stable.     

Instability of Waves in Magnetized Vortex-Like Ion Distribution Dusty Plasmas

A modified Zakharov-Kuznetsov equation for small but finite dustic waces in a magnetized votex-like ion distribution dusty plasma is obtained in this paper.It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.     

Magnetic ordering of the bond—diluted two—dimensional mixed spin Ising system

Numerical and analytical results are presented for the magnetic ordering in a bond-diluted spin-1/2 and spin-1 mixed transverse Ising system with a single-ion anisotropy on a honeycomb lattice.Special emphsis is placed on the magnetic ordering under the bond dilution and percolation threshold.We discuss in detail the influence of transverse fields of different sublattics on the normal magnetic ordering and on the magnetic ordering induced by single-lon anisotropy.We find that the magnetic ordering of a system exhibits an explicit difference when receiving the transverse field.This phenomenon has not been revealed in previous reports.     

Generation of entangled TEM_(01) modes with periodically poled KTiOPO_4 crystal

Spatial quantum optics based on the high-order transverse mode is important for the super-resolution measurement and quantum image beyond the shot noise level. Quantum entanglement of the transverse plane Hermite–Gauss TEM_(01) mode has been demonstrated experimentally in this paper. Two squeezed TEM_(01) modes, which are generated by a pair of degenerate optical parametric amplifiers(DOPA) with the nonlinear crystals of periodically poled KTi OPO_4, have been combined to produce TEM_(01) mode entanglement using a beam splitter. The 1.5 dB for the sum of amplitude and 1.2 dB for the difference of phase below shot-noise level is achieved with the measurement system of a Bell state detection.     

Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge

By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation for unmagnetized dusty plasmas,It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dust charge are stable even there are some higher order transverse perturbatoins,There are only rarefactive solitary waves for this system which has been verified analytically in this paper.     

Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed

We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.     

Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system

The projection of the chaotic attractor observed from the Lorenz system in the $X$--$Z$ plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined.In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi--Sugeno (TS) fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex (two-wing) butterfly attractors observed from this system in the three dimensional (3D) $X$--$Y$--$Z$ space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.     

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.