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 the further exploring routes to turbulence.     

On Integration of the Nonlinear d’Alembert-Eikonal System and Conditional Symmetry of Nonlinear Wave Equations

Abstract

We study integrability of a system of nonlinear partial differential equations consisting of the nonlinear d’Alembert equation □u = F (u) and nonlinear eikonal equation u _xµ u _x µ = G(u) in the complex Minkowski space R(1, 3). A method suggested makes it possible to establish necessary and sufficient compatibility conditions and construct a general solution of the d’Alembert-eikonal system for all cases when it is compatible. The results obtained can be applied, in particular, to construct principally new (non-Lie, non-similarity) solutions of the non-linear d’Alembert, Dirac, and Yang-Mills equations. Solutions found in this way are shown to correspond to conditional symmetry of the equations enumerated above. Using the said approach, we study in detail conditional symmetry of the nonlinear wave equation □w = F ₀(w) in the four-dimensional Minkowski space. A number of new (non-Lie) reductions of the above equation are obtained giving rise to its new exact solutions which contain arbitrary functions.     

Enhanced Nonlinear Absorption and Optical Limiting Properties of Organic Material ZnTBP—CA—PhR in a DA—ET System

Nonlinear absorption of the organic material Zn-tetrabenzoporphin-cronicacid-phenonxy resin(ZnTBP-CA-PhR) in the donor-acceptor energy-transfer(DA-ET) system is investigated by the irradiation of Ar^ laser on its solid film.A reverse saturable absorption and an enhanced second reverse saturable absorption called the rereverse saturable absorption are observed in a visible wavelength range.The high performance of optical limiting of the sample possessing low input threshold and an over 95% linear transmission ratio are observed.The physical mechanism of rereverse satruable absorption is analysed by a five-level rate-equation simulating.According to the Huygens wave diffraction principle and the combination of Kerr effect,thermo-optic effect and optical absorption variation,a mathematical model for the optical limiting of ZnTBP-CA-PhR film limiter is established and the theoretical simulating gives a good agreement with the experimental results.     

The Analysis and Improving of the Microwave Exciter in the Lower Hybrid Wave System

When we carry out lower hybrid wave heating and current driving plasma experiment at tokamak, we need mega-watt order of microwave power. The microwave signal at frequency of 2450 MHz is generated by a microwave exciter. According to the experiment＇s demands, the microwave exciter must provide output power of 1.5～ 2. 5 W with stabilized frequency and amplitude tobe used as the klystron input. Being amplified by the klystron, the microwave signal is transmitted through the transmitting system to the antenna and is emitted into the HL-2A tokamak. So we can see that the microwave exciter＇s function is very important to the lower hybrid wave heating and current driving plasma experiment.     

Effects of External Magnetic Field on Propagation of Electromagnetic Wave in Uniform Magnetized Plasma Slabs

Absorbers and reflectors of electromagnetic waves have many applications, and so the interactions between electromagnetic waves and low-temperature plasma, particularly numerical analysis of reflection, absorption, and transmission of electromagnetic waves in unmagnetized, magnetized, nonuniform, and uniform plasma, have been a topic of intensive research. For instance, Laroussi numerically evaluated the interactions between electromagnetic waves and a uniform magnetized plasma cylinder, and Helaly and Yeh studied the scattering from nonuniform magnetized plasma cylinders.     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

Electron Spin Pairing and Excitations in High—Tc Superconductors

Effective spin coupling between conduction electrons mediated by local Cu moments in the doped CuO2 plane may induce the instability of the normal states of conduction electrons and pairing at Cu stes,where the superexchange interaction between local moments influenced by hole doping has been found to be Ising-like in recent experiments.By a mean field approach,we show that spin pairing and strong pair-pair interaction in the doped antiferromagnetic ordered Ising-like CuO2 plane gives rise to high-temperature superfluid condensation and the exceptional features of quasi-particle excitation in cuprates such as spin gap,pseudogap,and the linear temperature dependence of resistivity ρab in the normal states.     

Wave Grouping of a Drifting Spiral Wave in the Presence of an External Field

The phenomenon of wave grouping, in which the dense waves and the sparse waves can form groups in front of the spiral tip when the spiral wave is meandering, has been reported in a chemical reaction system recently. We present a method to realize the phenomenon of wave grouping by applying an external field to the system. The numerical simulations are carried out on the basis of the FitzHugh-Nagumo equations.     

New Cnoidal and Solitary Wave Solutions of Coupled Higher-Order Nonlinear SchrSdinger System in Nonlinear Optics

The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.     

Inversion of Rayleigh Wave in a Stratified Half Space

Inversion of Rayleigh waves is studied for the first time by using the genetic algorithm based on the intensities of the fundamental and/or higher modes. The relations of all modes to the medium structure are investigated. It is emphasized that the higher modes and mode jumping should be considered in the inversion when the low-velocity     

Mechanical and Magnetostrictive Properties of Fe—Doped Ni52Mn24Ga24 Single Crystals

To improve the magnetic and mechanical properties of a Heusler alloy of Ni52Mn24Ga24,iron was doped with some cotents,Single crystals of the pseudoquaternary Heusler alloy of Ni52Mn8Fe15Ga24 have been synthesized for mechanical and magnetostrictive measurements.The magnetostriction loops and stress-strain curves were measured under different coupled magnetic-mechanical loads.The experimental results show that the brittleness of the sample is clearly improved and Yong‘s modulus of 13.7GPa is obtained in the [001] direction due to the part substitution of Fe for Mn.Furthermore,the toughness and Vickers hardness of the sample are also given by use of the indentation technique.     

Submergence and Control of Dark Soliton in a Dispersion—Managed System with Random Dispersion Map

Random dispersion map is considered in a dispersion-managed dark soliton system,its influence on soliton propagation and interaction is discussed.It is found that the random dispersion map results in large sidebands leads to submergence of dark soliton,and enhances the interaction between solitons.Finally,nonlinear gain is introduced to suppress the influence effectively.     

Symmetries and Similarity Reductions of a New （2＋1）-Dimensional Shallow Water Wave System

The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.     

Smooth and Peaked Solitary Wave Solutions of the Broer–Kaup System Using the Approach of Dynamical System

The bifurcations of traveling wave solutions of the Broer–Kaup system are investigated and all possible exact parametric representations of the smooth and peaked solitary waves are presented.     

Bifurcation of a periodic instanton and quantum－classical transition in the biaxial nano－ferromagnet with a magnetic field along hard axis

Crossover from classical to quantum regimes of the barrier transition rate in a biaxial ferromagnetic magnet with a magnetic field applied along hard anisotropy axis is investigated. We show that the type of action-temperature diagrams can he determined by counting the number of bifurcation points. The model possesses not only the known type I and Ⅱ, hut also the interesting type Ⅲ and Ⅳ of transition which do not occur in general.     

Negative Dispersion of Lattice Waves in a Two—Dimensional Yukawa System

Collective motion modes existing in a two-dimensional Yukawa system are investigated by molecular dynamics simulation.The dispersion relations of transverse and longitudinal lattice waves obtained for hexagonal lattice are in agreement with the theoretical results.The negative dispersion of the parallel longitudinal wave is demonstrated by the simulation,and is explained by a physical model.     

Quantum and Classical Evolutions of a Nonautonomous Dynamical System—A Comparison

The influence of moving boundaries on the stability of quantum Hamiltonian systems, in particular on the dynamics of quantum versions of the classical Pustilnikov model, is investigated (the latter consists of a masspoint bouncing above an oscillating plate under the influence of constant gravity.) It is shown that, in contrast to the classical Pustilnikov model, generic time-periodic boundary conditions (including the Dirichlet condition) on the quantum models do not allow unlimited energy gain (speeding up) of these systems.     

Parameter Identification and Tracking of a Unified System

The unified chaotic system contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum and the Lu system as a special case.The parameter identification and tracking problem of the unified system are further investigated.In particular,a novel controller is designed for avoiding the divergence of the factor 1/x.Numerical simulations are provided to show the effectiveness of these methods.     

Influence of Atomic Motion on a Microlaser in an Optical Standing—Wave Cavity

We study the microlaser in an optical standing-wave cavity injected with two-level atoms.The results have shown the obvious influence of atomic centre-of-mass motion on the microlaser,such as the photon distribution,the linewidth and the frequency shift.It was found that when the momentum of atoms is comparable to that of photons,the influence of atomic motion is dominated and the number of photons in the microlaser can be greatly enhanced,owing to part of the atomic kinetic energy being transferred to the resonator.This work provides a comparison of the related studies on the atomic motion under special assumptions.     

Direct Evaluation of Transition Amplitude Using Determinant of Wave Operator in One-Dimensional Potential Scattering System

A determinantal formula is developed for direct evaluation of transition amplitude without solving the wave equation in a one-dimensional potential scattering system. Our formulation is 5ased on the principle that a desired quantity can be extracted from the wave operator, which is the master operator maintaining all the information of the system. This principle is tested in a simplified system, i.e,, in a one-dimensional potential scattering system. We are now developing a formula for direct evaluation of near-field amplitude to design a system, in which local field enhancement is desired.