With the help of a known Lie algebra, two new high order Lie algebras are constructed. It is remarkable that they have different constructing approaches. The first Lie algebra is constructed by the definition of integrable couplings, the second one by an extension of Lie algebra. Then by making use of Tu scheme, a generalized AKNS hierarchy and another new hierarchy are obtained. As a reduction case of the first hierarchy, a kind of coupled KdV equation is presented. As a reduction case of the second one, a new coupled Schr?dinger equation is given.

In this paper, the existence of periodic orbits and the non-existence of limit cycles for the second-order autonomous Birkhoff system are studied. Further the existence of algebraic limit cycles for a generalized second-order autonomous Birkhoff system is studied.

In this paper, using feedback linearizing technique, we show that a Lorenz system can be considered as a cascade system. Moreover, this system satisfies the assumptions of global stabilization of cascade systems. Thus continuous state feedback control laws are proposed to globally stabilize the Lorenz system at the equilibrium point. Simulation results are presented to verify our method. This method can be further generalized to other chaotic systems such as Chen system,coupled dynamos system, etc.

Determining the input dimension of a feed-forward neural network for nonlinear time series prediction plays an important role in the modelling. The paper first summarizes the current methods for determining the input dimension of the neural network. Then inspired by the fact that the correlation dimension of a nonlinear dynamic system is the most important feature of it, the paper presents a new idea that the input dimension of the neural network for nonlinear time series prediction can be taken as an integer just greater than or equal to the correlation dimension. Finally, some validation examples and results are given.

Neutronics studies for a solid target have been done with Monte Carlo high-energy particle transport code NMTC/JAM, when the proton beam with high kinetic energy bombards the target. The effect of the main parameters of the target on the neutron flux is discussed to optimize the target, which will be used for the concept design of the target of spallation neutron source. A target with its aspect ratio 1.5:1 or 2:1 gives the highest neutron flux. Tungsten is the most acceptable material from the technical and economical points of view. Beryllium as a moderating reflector can increase the neutron flux effectively.

The electron density at the nucleus, ρ(0), and the radial expectation values, (-2≤n≤10), of the ground state for the lithium isoelectronic sequence are calculated with a full core plus correlation (FCPC) wavefunctions. By using these obtained expectation values, the accurate inequalities of the electron density at the nucleus and the radial expectation values derived by Gálvez and Porras for these systems are examined and verified. The final results show that FCPC wavefunctions used in this work can give satisfactory results in full configuration space.

Various types of moments have been utilized to recognize image patterns in a number of applications. Multi-distortion invariant－radial harmonic Fourier moments were investigated in the recognition of cell smear images. Image recognition experiments showed that radial harmonic Fourier moments are not only highly concentrated image features but also have a good property of antidistortion and antinoise. They may be used in fast and accurate automatic cell recognition.

The model of stochastic perturbation is built up systematically in quasi-ideal dispersion-managed soliton system, its influence on soliton propagation is investigated by both the variational approach and the numerical simulation, and it is found that the stochastic perturbation leads to disintegration of soliton and enhances the interaction between solitons. The nonlinear gain and filter are introduced to suppress effectively the influence on both soliton propagation and interaction.

Using the principle of diffusion-limited aggregation (DLA), a new model is introduced to simulate the displacement of one fluid by another in porous media. The results agree with experiments, apparently they do not leave out film-flow phenomena. Simultaneously, we also present a new numerical method to treat our results by the lattice Boltzmann method (LBM). All these will be helpful for analysing similar subjects.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

By using an expansion technique based on the tokamak ordering, the Grad－Shafranov equation is analytically solved for tokamak equilibrium sustained by a full bootstrap current. This approximate approach is suitable for equilibria with non-circular cross-sections of modest ellipse and triangular deformations. As an input parameter set, the plasma pressure profile and the electron and the ion temperature profiles can be selected as arbitrary functions of the averaged minor radius. Equilibrium properties of this plasma are discussed.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy, Lacks and Shukla is reformulated with explicit physical meanings. It is shown that the quantum effect is important at low temperature, it can be treated in the harmonic framework; and the anharmonic effect is important at high temperature and tends to zero at low temperature, it can be treated by using a classical approximation. The alternative formulation is easier for various applications, and is applied to a Debye-Grüneisen solid with the generalized Lennard-Jones intermolecular interaction. The expressions for the Debye temperature and Grüneisen parameter as a function of volume are analytically derived. The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal-pressure with the nearest-neighbour Lennard-Jones interaction, and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction. The theoretical results are in agreement with the experiments.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Chiral molecules griseofulvin were disseminated homogeneously in poly methyl metahcrylate (PMMA) host, which agglomerate from methyl metahcrylate and N, N-dimethyl formamide dimethyl acetal, using benzoyl peroxide as a catalyst. So the chiral organic glass has been manufactured successfully. Its optical rotatory were investigated from a solution state to a solid state. The results of measurement show that the chiral parameter of the chiral organic glass is 2.65×10^{-7} and its specific rotation has increased compared with its solution condition. Its infrared spectra property has been measured by Fourier transformation infrared spectrometer. The results show that the chiral molecules fill in the pore of the network structure in the organic glass, which hardly link with the host.

Absolute band gaps can be created by lifting the degeneracy in the bands of a photonic crystal. To calculate the band structure of a complicated photonic crystal generated by e.g. symmetry breaking, general forms of all possible linear operations are presented in terms of matrices and a procedure to combine these operations is given. Other forms of linear operations (such as the addition, subtraction, and translation transforms) are also presented to obtain an explicit expression for the Fourier coefficient of the dielectric function in the plane-wave expansion method. With the present method, band structures for various complicated photonic crystals (related through these linear operations) can be obtained easily and quickly. As a numerical example, a large absolute band gap for a complicated photonic crystal structure of GaAs is found in the high region of normalized frequency.

We study the quantum dynamics of a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We demonstrate that under weak damping of the quantized field, the collapse-revival phenomena can exist in this system, and the oscillations of the collapse and revival depend sensitively on the initial state of the single-mode quantized field and the damping rate κ. We also demonstrate that this system can show the beats phenomena.

A modified Yafet－Kittle model is applied to investigate the magnetic properties and magnetic phase transition of the intermetallic compound GdMn_2Ge_2. Theoretical analysis and calculation show that there are five possible magnetic structures in GdMn_2Ge_2. Variations of external magnetic field and temperature give rise to the first-order or second-order magnetic transitions from one phase to another. Based on this model, the magnetic curves of GdMn_2Ge_2 single crystals at different temperatures are calculated and a good agreement with experimental data has obtained. Based on the calculation, the H－T magnetic phase diagrams of GdMn_2Ge_2 are depicted. The Gd－Gd, Gd－Mn, intralayer Mn－Mn and interlayer Mn－Mn exchange coupling parameters are estimated. It is shown that, in order to describe the magnetic properties of GdMn_2Ge_2, the lattice constant and temperature dependence of interlayer Mn－Mn exchange interaction must be taken into account.

The outstanding hard-magnetic properties are reported of Sm_3Fe_{28.1-x}Co_xMo_{0.9} compounds with x=12, 14, 16. In this alloy system, only a small amount of Mo is needed to stabilize the 3:29 structure so that the magnetic properties are not seriously affected by the presence of this nonmagnetic element. Substitution of Co for Fe leads to a significant increase of the magnetic anisotropy, and for x≥14 the easy magnetization direction changes from easy plane to the easy axis. In this alloy system, the compound Sm_3Fe_{12.1}Co_{16}Mo_{0.9} is a very promising candidate for permanent magnet applications. Its room temperature saturation magnetization (μ_0M_s=1.5 T) and anisotropy field (B_{an}=6.5 T) are comparable to the values for Nd_2Fe_{14}B (μ_0M_s=1.6 T and B_{an}=7 T). However, the Curie temperature of Sm_3Fe_{12.1}Co_{16}Mo_{0.9} is 1020 K, which is appreciably higher than that for Nd_2Fe_{14}B (T_C=588 K).

We have demonstrated that the bulk-like contribution to tunnelling magnetoresistance (TMR) exists in the magnetic tunnel junctions, and is determined by the tunnelling characteristic length of the ferromagnetic electrodes. In the experiment, a wedge-shaped CoFe layer is inserted at the interface between the insulating barrier and the reference electrode. It is found that TMR ratio increases from 18% without CoFe layer to a saturation value of 26.5% when the CoFe thickness is about 2.3 nm. The tunnelling characteristic length, l_{tc}, can be obtained to be about 0.8 nm for CoFe materials.

We have prepared Er^{3+}-doped borotellurite glasses using conventional melting and quenching method. The absorption spectrum analysis is performed on the basis of Judd-Ofelt theory. The effects of B_2O_3 on the spectroscopic parameters such as intensity parameters, line strengths of electric-dipole transitions, and spontaneous emission probability are discussed.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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