From the viewpoint of equivalent sources, the ferromagnetic hull of naval vessels is regarded as a magnetic charge layer, and a Fredholm integral equation of the first kind relating the layer with the measurements of magnetic field sensors is developed. After the discretization of the integral equation, a system of linear equations is obtained which is solved by generalized inverse matrix, and the condition number is employed to assess whether the system is ill-posed. Then the field caused by the hull at an arbitrary point in the space is predicted by the calculated layer. A numerical simulation shows that our method can precisely identify the magnetization to predict the field. And finally a ship model is used to verify the method.

By now, the negative refraction phenomenon occurs only in the microwave band in the left-handed materials, and this frequency band is called resonant frequency band. The application of the left-handed materials is greatly limited because the resonant frequency is low, and the source of wave is usually sun light or visible light.How to shift the resonant frequency from low frequency to high frequency, even to the visible light band, is an important and urgent research problem. Many parameters of the periodic structures will greatly affect the resonant frequency, including the shapes and sizes. The resonant frequency is shifted by adjusting the cell size.The relation that the resonant frequency band can be shifted and broadened from low frequency to high frequency with the reducing cell size, is obtained by simulation and experiment.

We perform a numerical simulation of marine controlled-source electromagnetic （MCSEM） responses in a layered anisotropic seabed using integral equation method. Firstly, we use the operator theory to deduce the contraction integral equation, which is always convergent regardless of any parameters, for it satisfies the contraction mapping condition. Then we introduce the subdomain multigrid and quasi-linear approximation to improve the computation efficiency. We also validate the accuracy and efficiency of the algorithm by synthetic numerical modelings. Finally, we simulate the three-dimensional MCSEM responses in the layered anisotropic seabed, and investigate the effects of anisotropy.

Optical feedback characteristics of frequency modulated microchip Nd:YAG lasers with anisotropic external cavity are investigated. With isotropic optical feedback, the modulation frequency of output intensity is proportional to the ratio of external cavity length to internal cavity length. With anisotropic optical feedback, the laser polarization periodically hops between two orthogonal directions with equal bandwidth. The times of polarization flipping in the longitudinal mode bandwidth is proportional to the ratio of external cavity length to internal cavity length, resulting in double frequency of original fringes. The theoretical analysis based on Fabry-Perot cavity equivalent model is in good agreement with the experimental results. The potential applications of this phenomenon in precision measurement are discussed.

A model for a kind of non-spherical particles with elliptical cross section is established, and their phase functions are obtained. Based on the radiative-transfer equation, considering the shape and size distribution, we obtain the multiple light scattering of this kind of particles. Our results are in agreement with the earlier results in two special cases, which verifies that our method is reliable. The calculation and analysis show that the distribution of multiple scattered intensities of non-spherical particles is flatter than that of the spherical particles. The larger the shape parameter or the size of particles is, the smaller the scattering angle is. The wider the size-distribution or shape-distribution is, the flatter the angular distribution of the light intensity is. The angular distribution of the light intensity becomes flatter with the increasing optical thickness. The multiple scattering intensity at a scattering angle at first increases and then decreases with the increasing optical thickness. A new potential way of studying the multiple light scattering of actual non-spherical particles is provided.

Propagation characteristics of laser beams are examined in fractional self-imaging planar waveguides. A potential approach to laser beam combining is proposed by application of planar waveguides with fractional self-imaging. The influences of phase mismatch between laser beams on laser beam addition are discussed. The numerical simulation for two lasers with average power of 300 W shows that the beam addition in fractional self-imaging planar waveguide can improve the parameter M^{2} of combined beam effectively. The sensitivity of beam addition to the phase mismatch between laser beams has been reduced obviously.

The principle of a polarization interference imaging spectrometer based on Wollaston prism is presented. The accurate optical path difference, splitting angle and fringe location plane of single Wollaston prism in four different conditions are calculated by wave-normal tracing method, and the theoretical formulas are introduced. The accurate values and approximate values of the optical path difference, the splitting angle, the fringe location are compared by computer simulation. The results show that the influences of wedge angle, incident angle and incident position on the accurate values and the approximate values are greatly different. The selection range of the wedges angle and the incident angle are deduced according to the accurate value, and the deviation of fringe location plane and its influence on Fourier transform lens are analysed. This study provides a theoretical and practical guidance for the study, design, modulation, experiment and engineering of the polarization interference imaging spectrometers.

By recording the interference patterns of the speckle fields and the reference beam with the charge coupled device （CCD）, and by using the digital Fourier transform technique, the amplitude and the phase distribution of the speckle fields are experimentally extracted. We find that at the tangential points of the zero curves of the real and the imaginary parts, a new kind of speckle phase singularities may appear. Different from the conventional singularities at the zero crossings of the real and imaginary parts with the monotonically spiral change of phase, this new kind of singularities has the property that the phase undergoes an increase and then a decrease around the singular point with nearly a symmetric distribution. We introduce the concept of quasi twin phase vortices to explain the formation of the new kind of phase vortices. Based on a theoretical study of the longitudinal autocorrelation function of the speckle intensities, we experimentally observe the propagation of the phase vortices of speckles. It is found that in planes at different propagation distances but within a longitudinal correlation length, the real and the imaginary parts of the complex speckle field vary considerably, but the position of the phase vortices and the angle of the zero crossings of the real and imaginary parts remain unchanged.

The distribution of pump light and signal light power of Nd^{3+}-doped fiber amplifier along the fiber is numerically simulated. The Nd^{3 +}-doped polarization-maintaining fiber amplifier is experimentally studied, which is pumped by 808nm semiconductor laser. The enlargement factor of small-signal is 300（the gain is 25dB）, and the steady 5W amplificatory pulse is obtained by using the self-made Nd:YAG passive mode-locking laser as seed source. The 86142B-type spectrograph and TDS5104 oscillograph are employed to detect the output laser, and the output power is measured by power meter.

A numerical model of intracavity second harmonic generation（SHG） is constructed considering the effect of phase mismatching and birefringent walk-off in nonlinear crystals for optically pumped semiconductor vertical-external-cavity surface-emitting laser（OPS-VECSEL）. The influences of the crystal length and the pump power on the SHG output power for some nonlinear crystals, such as BBO, LBO and PPLN, are studied in detail. The results are in good agreement with the experimental data.

The oscillation mechanism of dual-wavelength Nd:YAG Q-switched laser with two-mirror resonator is studied on the basis of the rate equation. The characteristics of the dual-wavelength laser are discussed by analysing the competition process with different transmissivities. Results show that the oscillating time of the Q-switched pulse laser for 1319nm laser is delayed relative to that of 1064nm. The 1319nm Q-switched laser is formed finally from the first relaxation oscillation spike after the Q-switch opening, i.e. it restrains the rest relaxation oscillation spikes. The transmissivity of relatively balanced output energy is theoretically obtained.

The focusing properties of a novel type of beam, i.e. an anomalous hollow beam focused by a spherically aberrated aperture lens, are studied by using the Debye formula. It is shown that， the shape of the anomalous hollow beam does not keep unchanged upon propagation. However, the anomalous hollow beam at a certain position can keep its initial profile nearly unchanged by selecting the suitable truncation parameter and spherical aberration. The motion, creation and annihilation of phase singularities occur in the focal region, which depends on the truncation parameter,the spherical aberration and the half angle of the aperture lens. The saddle points may appear, and the annihilation process of a pair of phase singularities is accompanied by the annihilation of a pair of saddle points in the spherical aberration-free case, which leads to the subwavelength structure. The results are illustrated by numerical examples and are compared with the results of previous work.

A cylindrical micro-cavity was made by immersing a silica optical fiber into a low refractive index dye solution.Pumped by evanescent wave along the fiber axis, dye gain was confined in the evanescent field of whispering gallery mode （WGM） of the fiber, which led to a high pumping efficiency and a long gain distance along the fiber axis. When the fiber was immersed into Rhodamine 6G and Rhodamine B dye solution with the same concentration of 8×10^{-4}mol/L but separated to two parts, WGM laser emissions in the wavelength ranges of 567—576nm and 592—600nm were observed; when immersed into Rhodamine B dye solution with two concentrations of 8×10^{-4} and 8×10^{-3}mol/L, WGM laser emissions in the wavelength ranges of 588—595nm and 600—618nm were observed. WGM laser emission in two different wavelength ranges in a single optical fiber was realised, which formed a new kind of WGM laser, the two-wavelength-range WGM fiber Laser.

A novel mutual injection phase-locking fiber laser combining technique is proposed， based on a corner-cube and a beam splitter with reflectivity of 50% at 45°， and the mutual injection phase-locking principle is introduced. Mutual injection phase-locking of two individual double clad fiber lasers is experimentally realized, steady interference stripes with high contrast ratio（about 0.57）are observed and more than 10W output power is obtained, which indicates that the power combining efficiency is 76%. Successful attempts of phase lock show that this mutual injection-locking method is a promising technology in the field of fiber laser coherent and the output power can be further scaled.

By taking the strong two-photon absorption 4,4′-bis （dimethylamino） stilbene molecules as medium, the propagation of femosecond laser pulses in this medium is simulated by numerically solving the Maxwell-Bloch equations using an iterative predictor-corrector and finite-difference time-domain method. The influences of time-dependent ionization on two-photon absorption and optical power limiting behavior are emphatically investigated. The numerical results show that the nonlinear interactions between the pulses and the medium and the corresponding spontaneous emission become weaker when the time-dependent photoionization is considered. The effects of photonionization on the main pulse become more evident as the amplitude of input electric field is increased. When the photonionization cross section is larger, the dynamic optical limiting range becomes broader, which demonstrates that the limited photonionization ability is favorable for the optical power limiting. Furthermore, the propagating-distance dependence of the dynamical behavior of the ultrashort laser pulse in the medium is observed.

We analyse the stimulated Brillouin scattering （SBS） slow light using double broadband pumps in a single mode fiber. A new SBS gain spectrum tailoring method is proposed using two Gaussian-shaped broadband pumps with different powers and spectral widths, and the central frequency interval of them is carefully set at two Brillouin frequency shifts to make sure that the gain of one pump has the same center with the loss of the other. The top of the gain spectrum of the strong pump beam can be counteracted by the loss spectrum of the weak pump beam to construct a flat top gain spectrum. We give the optimized conditions of the laser powers and spectral widths between two broadband pumps to obtain a flat gain. Distortions of signal pulse under this flat top gain are studied and compared with that obtained using a single broadband pump. We find that the flat top gain profile can effectively reduce the pulse distortions.

A transmission line model capable of predicting the reflection phase of high impedance surfaces in normal incident is proposed. The surface impedance of high impedance surface （HIS） can be regarded as the effective capacitive impedance of patch array in parallel with the inductive impedance of substrate layer, and the effect of vias conductor can be ignored at normal incidence. Results of the a nalytical model agree well with the HFSS simulated results. HIS with different parameters are fabricated and tested, the reflection phase of HIS predicted using the transmission line model agree well with the measured results, which proves the validity of this transmission line model.

The dipole mode in triangular photonic crystal single defect cavity is degenerate. By deforming the lattice in photonic crystal we can obtain non-degenerate dipole modes. Lattice deforming in the whole photonic crystal destroys the characteristic of symmetry, so the distribution of the electromagnetic field is affected and the polarization of the electromagnetic field is also changed. Lattice deforming divides the degenerate dipole mode into the x-dipole mode and the y-dipole mode. It is found that the non-degenerate modes have better properties of polarization. So the high polarization and single dipole mode photonic crystal laser can be achieved by deforming the lattice of photonic crystal. In this paper, we simulated the cavity in photonic crystal slab and mainly calculated the quality factor of x-dipole mode under different deforming conditions and with different filling factors. The properties of polarization of x-dipole and y-dipole modes are also calculated. It is found that the ratio of intensities of E_{x} to E_{y} in x-dipole mode and that of E_{y} to E_{x} in y-dipole mode are 44 and 27, respectively.

The structure of the parallel metallic slabs with middle-part-indentation is based on the parallel metallic wires. The permittivity of the structure is negative in a certain frequency range because of the effect of the plasma. And the strong magnetic resonance occurs in the special frequency range because the middle-part-indentation is introduced in the parallel metallic slabs. The result of simulation shows that the structure composed of ceramic alumina has negative permittivity and permeability in the X-band. The range of the double negative （ε<0,μ<0） varies with the resonance frequency. Theoretical analysis, which is in agreement with the results of simulation, indicates that the resonance frequency is related with the width of metallic slaps, height of indentation and the width of the middle-part of the structure.

We describe a self-referencing two-path interferometer designed to measure the carrier-envelope phase stability. In experiment, we measure the carrier-envelope phase （CEP） stability of a home-made infrared tunable OPA laser pulses with the self-referencing two-path interferometer. When the wavelength of the incident pulses is 1.6 μm, the CEP fluctuation is 115 mrad （rms） in 100 seconds. The interferometer can provide an accurate and quick measurement of the pulse CEP.

By increasing the local temperature at different positions along the argon gas-filled tube, the difference in filament and spectrum broadening was compared in this paper. The experimental results show that the filament can be controlled by increasing the local temperature of the gas-filled tube. The best way to realise the maximum of such a influence is to heat at the focus point. Spectrum broadening will be narrow with the increase of the local temperature.

Two Rugate filters for compensating gain narrowing are designed separately based on the gain characteristics of Ti: sapphire amplifier and Nd: glass amplifier. The Gauss spectral shaping function is selected as the compensation modulation function. Characteristic matrix method is used to analyse the spectral response of the Rugate filter approximately. Amplification using Rugate filter spectral compensation is analysed numerically. Results show that they satisfy the compensation requirements well and can be used as the spectral compensation filters.

The filters with low angle effect are composed of high index dielectric layers and metallic layers laid alternately. When used in the case of oblique incidence or large cone angle incidence, this filter reduces shift of central wavelength significantly while still maintaining its filter characteristics. Theoretical and experimental studies show that such a novel filter can be used in the situation of both large incident angle and cone angle.This effect is due to the usage of high index material and its induced transmittance.

A novel wavelength shift detection scheme for use in fiber Bragg grating sensing systems is proposed. The structure of the polarization maintaining fiber loop mirror is studied and its theoretical model is established. In addition, the distribution characteristics of the input light wavelength and the output power are analysed. Moreover, numerical simulation and experimental validation are also performed. The results show that the device has simple structure, high stability and high detection precision. The measuring range and the precision can be adjusted by varying the parameters of the fiber loop mirror. In the demodulation range larger than 1 nm, the average precision of the wavelength demodulation is lower than 1 pm.

The interaction between liposomes and cells under ultrasound exposure was theoretically and experimentally studied. We experimentally developed liposomes containing fluorescent materials, and measured the efficiency of drug delivery in a suspension containing liposomes and cells under 1 MHz ultrasound excitation for 40 s. Results demonstrated that the sonicated samples were superior to the control group （without ultrasound） in absorbing fluorescent materials and the capacity was improved by 8.78% under the excitation of ultrasound at an acoustic pressure amplitude of 0.24 MPa. Finally, the potential mechanisms of ultrasound enhancement was discussed with respect to the changes of velocity and diameter of liposomes induced by ultrasound.

The homogeneous solutions to the governing difference equations derived from energy variational method were used as the displacement patterns of finite segment. A finite segment model considering the initial curvature, bending,torsion,shear lag and distortion was established. The stiffness matrix and load column matrix were obtained based on the directed stiffness method and the working energy principle. A finite segment method was presented to calculate the shear lag effects with multi-span continuous curved box girder generally used in engineering. A perspex glass model of a two-span continuous curved box girder was made.The test on the perspex model were performed to study the shear lag effects respectively under concentrated load and uniformly distributed load. The calculation results of finite segment method were in agreement with the experimental results and results of finite element method, which verifies the accuracy of the finite segment method.

A numerical method for extracting parameters of extreme sea wave and calculating its dispersion relation is presented. The nonlinear sea surface can be regarded as waves whose wave numbers and frequencies change with temporal and spatial points. At every point, the height of sea surface can be interpolated by the value of an extending sine wave whose parameters （such as wave numbers and frequencies） are constant. From the first order and the second order derivative of extreme wave, we can extract wave numbers, frequencies, and amplitudes of the extreme wave. The numerical amplitude results show that this method is valid. Comparing values of ω^{2}/k with g, we can find that the nonlinear area does not lie in the area of extreme waves, but lies very closely to both sides of them. The corresponding wave heights in these areas are lower than that in the linear dispersion area. Compared with wavelet and Hilbert transform analysis method, our method has two advantages: Firstly, it saves much buffer capacity and CPU time. Secondly, it can supply disperse relationship of systems which other methods cannot supply. The disadvantage of this method is that, in the area of engineering application, it is only applicable to systems with coexisting temporal series data and spatial data.

The surface tension of a liquid is one of the basic factors determining cavitation and cavitation erosion. The expansion and contraction of cavitation bubble in liquids with different surface tensions are investigated experimentally, which are compared with theoretical analyses based on Rayleigh-Plesset equation. In the experimental study, cavitation bubble is induced by a laser pulse, the spatial evolution and velocity of the bubble wall in liquids with different surface tensions are detected by a fiber-optic diagnostic technique based on optical beam deflection. Experimental results show that the surface-tension forces hinder the bubble growth progress, so increasing surface-tension decreases the maximum bubble radii. On the other hand, the surface-tension forces speed up bubble collapse process. In larger surface tension cases, the bubble velocity is higher, and higher erosive power is produced.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

To study the micro-scale mechanical properties and failure behavior, and achieve the goal of “performance-oriented” design of microstructure and material performance prediction, in this study, computer simulation, micromechanics calculation and virtual failure analysis on microstructures of polycrystalline materials with multi-component and multiphase are realised by means of programming and finite element numerical simulation. Under the condition of creating representative volume element of microstructures of polycrystalline material and polycrystalline matrix composite that are constructed by material microstructure computer simulation software ProDesign, and based on the secondary development of the commercial finite element software ABAQUS, numerical calculation of micro-scale mechanics of microstructures is implemented. The results of the numerical simulation can be used to predict material performance, identify “material structure weakness”, evaluate initialization and propagation of microcracks of microstructures for heterogeneous materials and deduce the behavior of “virtual failure” of microstructure.

The Monte Carlo method with EAM potential is used to simulate the liquid Ni-15%Mo binary alloy system, from which the thermophysical properties hardly measured by experimental measurement can be obtained. The simulated surface tension of liquid Ni-15%Mo alloy at the melting temperature is 1.918 N/m, and the simulated temperature coefficient of surface tension as a function of temperature is σ=1.918-1.130×10^{-3}（T-T_{m}） N/m. Based on the simulated surface tension, the variation of viscosity and solute diffusion coefficient within the range of from 1500 K to 2000 K can be deduced. The result of the viscosity is η=0.895exp（2.209×10^{4}/RT） mPa·s, that is, the viscosity constant is 0.895 mPa·s, and the apparent activation energy is 2.209×10^{4} J/mol. The diffusion coefficient can then be obtained by the Stokes（Sutherland）-Einstein equation as D=9.803×10^{-8}exp（-3.643×10^{4}/RT） m/s^{2}， where the activation energy is 3.643×10^{4} J/mol. From the relationship between system energy and temperature, the specific heat of liquid Ni-15%Mo alloy at different temperatures can be determined to be C_{p}=37.313-1.425×10^{-2}（T-T_{m}） J·mol^{-1}·K^{-1}.

The creep behavior of a {［（Fe_{0.6}Co_{0.4}）_{0.75}B_{0.2}Si_{0.05}］_{0.96}Nb_{0.04}}_{96}Cr_{4} bulk amorphous alloy and effects of different loading rates on its creep deformation behavior were investigated using nanoindentation technique at room temperature. It is found that the creep deformation of this alloy is strongly dependent on the indentation loading rate: when the loading rate ranges from 3 to 24 mN/s, distinct creep deformation occurs; but when the loading rate decreases to 1 mN/s or 0.75 mN/s, the creep deformation is completely suppressed. The creep deformation behavior of the {［（Fe_{0.6}Co_{0.4}）_{0.75}B_{0.2}Si_{0.05}］_{0.96}Nb_{0.04}}_{96}Cr_{4} bulk amorphous alloy was modeled using the elastic-viscoelastic-viscous （EVEV） model and a high correlation coefficient （R） of 0.9392 was obtained, implying that this creep behavior studied can be well described by the EVEV model. Based on the EVEV model, the creep compliance and retardation spectrum, which are related to the interior structure of the bulk amorphous alloy, were further calculated by the EVEV model. Finally, the creep mechanism at room temperature was discussed in detail according to the analysis of the creep rate sensitivity index （m） as well as the observation on the morphology of indents using the atomic force microscope （AFM）.

The absorption behavior of copper atoms on the armchair （5,5） single wall carbon nanotube is investigated by the density functional theory. It is shown that the absorption on the outside nanotube is energetically preferred to that on the inside nanotube, Morever, the adsorbed copper atom on the top of carbon is more stable than that on the other outside sites. At the same time, the characteristic of the forming bond on the top of carbon between copper and SWNT is detailed. The absorption behavior belongs to chemical absorption, and based on the analysis of frontier orbital, it is shown that the new σ bond is mainly due to the interaction of 4s valence state of copper and coupling σ-π bond of SWNT. Furthermore, the calculated electron densities of two representative adsorption positions show that electron clouds overlap more on the top of carbon adsorbed copper atom， which further confirms that copper and carbon atoms can form chemical bond in a sense.

Based on the atomic force microscope observation of the three-dimensional mesostructure of Fe_{73.5}Cu_{1}Nb_{3}Si_{13.5}B_{9} alloy ribbon annealed at different temperatures, on the basis of experimental results of X-ray diffraction and the Mssbauer spectroscopy and theoretical results for this alloy ribbon, we systematically investigate the crystallization process of this alloy ribbon annealed at different temperatures, and propose a number of new concepts, such as the mesostructure with two-kinds of Nb-B framework, the agglomeration phase of the nanocrystalline grains, and the average numbers of nanocrystalline grains in unit volume. Finally, a hypothesis of the crystallization mechanism and the mesostructure model describing the crystallization process of this alloy are established. This model can be evolved to the two- or three-phase structure model.

Molecular dynamics simulation is used to study the thermal stability of cubic platinum nanoparticle. The simulated results show that the cubic nanoparticle first transforms into the truncated cube enclosed by {111} and {100} facets, and then transforms to the spherical one. Finally, it melts into liquid state. The critical temperature of shape transformation is about 1250 K according to the calculation of statistical radius. Cubic and spherical nanoparticles have the same melting point in spite of their different shapes.

An effective interatomic potential is crucial for molecular dynamics simulations. A more effective potential is proposed. One of the characteristics of this potential is the introduction of the parameter r_{eff} to calculate the electrostatic interactions among atoms. The pair-correlation functions and X-ray diffraction patterns of cubic and tetragonal Barium Titanium are derived from molecular-dynamics simulations with the use of the new potential function. Lattice constants and elastic constants are also calculated. The calculated results agree well with the experimental data, which suggests that this potential is promising in describing the thermodynamic or mechanic properties of Barium Titanium.

Based on the physical process of holes trapped in oxide and interface trap buildup induced by proton, a unified physics-based model of oxide-trapped charge and interface trap charge in MOSFET after ionizing radiation exposure as a function of radiation dose is proposed. This model predicts that the oxide-trapped charge density and interface trap charge density induced by radiation rays would be linear in dose at low dose levelss, and would deviate from linear relationship and tend to saturation at moderate to high dose levels. The change of these two kinds of charge induced by ionizing radiation as a function of radiation dose can be well described by the expressions proposed in this model. At last, the correlation between these two kinds of charge is discussed and a linear dependence is suggested at low dose level. This model gives insights into the trap generation in gate oxide induced by radiation, and provides a more accurate predictive model for radiation damage in MOS devices operated in space ionizing radiation environment.

New physical parameters “Y elastic constants" and their physical meanings are proposed at the first time. The Y elastic constants are applied to the polycrystalline materials with cubic system structural single crystals, and they are deduced and compared with the “X-ray elastic constants" of polycrystalline materials with cubic system structural single crystals. The expressions of mechanical elastic constants of polycrystalline materials based on Y elastic constants are in good agreement with that proposed by Krner.

The ab initio electronic structure optimization and total-energy calculations are used to study the equation of state （EOS） and elastic properties of fcc aluminum at zero temperature. We use the calculated energy of a solid as a function of the molecular volume fitting to the quasi-harmonic Debye model to obtain the non-equilibrium Gibbs function, then to derive the thermal equation of state （EOS） of the corresponding phase. The melting curve at different pressures is presented based on the Burakovsky-Preston-Silbar （BPS） model. All total-energy calculations are based on the average of local density approximation （LDA） and general gradient approximation （GGA）. The results show that the calculated EOS and pressure dependence of thermodynamics and melting curve are in good agreement with the shock compression and the diamond-anvil-cell （DAC） data within a wide range of pressure up to 225 GPa.

Hydrogen-free SiN_{x} films were deposited at N_{2} flow rate ranging from 1 sccm to 20 sccm by microwave electron cyclotron resonance plasma enhanced unbalance magnetron sputtering system. We studied the influence of N_{2} flow rate on the structural characteristics of deposited films in chemical structure, stoichiometry, composition at different depths in film, and hardness by using X-ray photoelectron spectroscopy and nano-indantation. The results indicate that the films deposited at low N_{2} flow rate are Si-rich structure. The films deposited at 2 sccm N_{2} flow rate show an excellent stoichiometry with 94.8% Si—N bond content and uniformity of composition in different depths. At the same time, the films display the highest hardness value of 22.9 GPa. The films deposited at high N_{2} flow rate contain too much N—Si—O bond and Si—O bond, which is caused by chemical absorption both on and in film in atmosphere. The films present N-rich structure. In this situation, the films display poor mechanical properties with hardness of only 12 GPa.

Nano-β-FeSi_{2}/a-Si layered structure was successfully deposited on Si （001） substrates using radio-frequency magnetron sputtering method. X-ray diffraction, transmission electron microscopy and photoluminescence （PL） analyses were used to characterise the structure, composition and photoluminescence properties of β-FeSi_{2}/Si multilayer films. The results show that the peak at wavelength of 1.53 μm is observed from Fe/Si multilayer films by PL at room temperature. Without annealing, The films are of （amorphous FeSi_{2}+ Nano-β-FeSi_{2} particles） / amorphous Si structure, whereas after annealing, the films are of β-FeSi_{2} particles/（crystal Si + amorphous Si） structure. Furthermore, the same PL intensity between as-grown and annealed samples indicates that identical luminescence property can be excited from amorphous FeSi_{2}+β-FeSi_{2} particles and β-FeSi_{2} particles. In this experiment, the peak at wavelength of 1.53 μm is also a further indication of the semiconducting properties of amorphous FeSi_{2}.

The scaling behaviour of surface roughness evolution of high rate deposited μc-Si:H by very high frequency plasma-enhanced chemical vapor deposition （VHF-PECVD） is investigated using spectroscopic ellipsometry （SE）. Films deposited at P_{g}=300 Pa with deposition rate of 5 ?/s, show abnormal scaling behavior with the exponent β of about 0.81, which is much larger than 0.5 of zero diffusion limit in the scaling theory. This implies that there are some roughening increasing mechanisms, and this roughening increasing mechanism is correlated with the shadowing effect.

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

The band structure and the optical properties of Ba_{0.5}Sr_{0.5}TiO_{3} are studied by the first principles method. The results show that the conduction band and the valence band are derived from the hybridization between titanium 3d orbitals and oxygen 2p orbitals. In the conduction band, titanium 3d orbitals play a primary role, while in the valence band, oxygen 2p orbitals play a primary role. The absorption coefficient is as targe as 10^{5}cm^{-1}, and the absorption is mainly localised in the low energy region. The refractive index n（0） equals 2.1. Our results are in good agreement with the experimental results.

Based on first-principles calculation of the electronic structure and transport properties, we study the electronic structure and transport properties of graphene nanoribbons （GNRs） with 585 divacancies defects. It is shown that because of the existence of 585 divacancies defects, there are defected band belts in the energy gap located at the defects for the zigzag graphene nanoribbon （ZGNRs） and their energy gaps will increase. The spatial orientations of the divacancies defects have effect on the electronic structure of the system. In addition, the influences of 585 divacancies defects on the transport properties of the ZGNRs with small energy gaps are great, while that on the transport properties of the ZGNRs with large energy gaps are small. And the spatial orientations of the defects have no obvious influence on the transport properties.

The geometry structure, band structure, partial density of states, mulliken changes, and electron density of zinc blende CdS and CdS:M（M=Mg, Cu） were studied systemically by the density functional theory（DFT） based on first-principles pseudopotential caculation. It is shown that the M-doped material has a smaller lattice constant, which results in a local lattice distortion. The band structure and density of states（DOS） were further calculated and analysed in detail. The results show that Cds doped with Mg, Cu can provid many states of holes. The p-type conduction was obtained. And Cu was a better p-type dopant than Mg.

Based on the framework of density functional theory，we employed the first-principles molecular dynamics to simulate the thermal decomposition of liquid nitromethane and obtained the time-evolution for the population of decomposition productions. We discussed the three possible reactions at the initial stage of thermal decomposition: intramolecule proton transfer reacton, intermolecule proton transfer reaction, and C—N bond rupture. We also studied the dynamic behavior of thermal decomposition of liquid nitromethane under different density （pressure） conditions. We found that the thermal decomposition of liquid nitromethane sensitively depends on the liquid density of pressure. A possible explanation was given.

Adopting a tight-binding electron-phonon interacting model, we investigated the collision between a negative polaron and a triplet exciton in polymers under the influence of different electric fields. The results show that, after the collision, the electrons of the system have the most probability of keeping the same configuration as it initially is. The electron confined in the polaron defect has some probabilities to be excited into the conduction band to form a free carrier， and the triplet exciton has some, even less, probabilities to be annihilated by the negative polaron to form an excited polaron in the collision. It is also found that the collision proccess can influence the stability of the polaron and there are new energy levels appearing in the gap after the collision. Because an excited polaron can decay radiatively to its ground state, the scattering process has influence on the efficiency of electroluminescence. These results will help us to understand the properties of polaron transport and electroluminescence in polymers.

ZnO nanowires with the average diameter of 20 nm and the length of longer than 10 μm were synthesized on GaAs substrate by chemical vapor deposition（CVD）. As-doped ZnO nanowires were obtained by annealing the samples at 600 ℃ for 30 min in oxygen. Single ZnO nanowire field effect transistors（FET） were fabricated by electron beam exposure and magnetron sputtering deposition and Ti/Au deposited as ohmic-contact electrodes. Based on the electrical properties of the single ZnO nanowire FET before and after annealing, we verified that p-type ZnO nanowire can be obtained by As doping effectively. The parameters of the single As doped ZnO nanowire FET were as follows: the transconductance was 35 nA/V, the hole density was 1.4×10^{18} cm^{-3}, and the mobility was 6.0 cm^{2}/V·s. We also obtained the photoluminescence spectrum of single As-doped ZnO nanowire: strong ultraviolet light at 383 nm, weaker yellow-green light, and red light due to the existence of As_{Zn}-2V_{Zn} shallow acceptors.

The characteristics of quantum transport through a four-terminal coupled-quantum-dot-molecular bridge are investigated theoretically by nonequilibrium Green’s function. The transmission probabilities of the electrons transported through the molecular bridge to every terminal are obtained.

We introduce a kind of surface plasmonic waveguide with double elliptical metallic nanorods. The dependence of the distribution of longitudinal energy flux density, the effective index and the propagation length of the fundamental mode with longer propagation length supported by this waveguide, on the geometrical parameters and the working wavelengths are analysed using the finite-difference frequency-domain （FDFD） method. Results show that the longitudinal energy flux density is distributed mainly in the middle area, which are formed by two elliptical metallic nanorods, and the longitudinal energy flux density is stronger closer to the arc sides of the metallic nanorods. The effective index and propagation length of the fundamental mode can be adjusted by the centric distance of two ellipses as well as the size of the two semiaxis. At a certain working wavelength, relative to the case of a=b, in the case of a<b, the size of the contact area of field and metallic surface is large, the interaction of field and silver is weak, the effective index becomes small, so the propagation length becomes large. With certain geometric parameters, relative to the case of λ=7050 nm, in the case of larger λ, the area of field distribution is large, the size of the contact area of field and metallic surface is also large, the interaction of field and silver is weak, the effective index becomes small, so the propagation length becomes large. This kind of metallic surface plasmonic waveguide can be applied to the field of photonic device integration and sensors.

Using the Keldysh nonequilibrium Green function and equation-of-motion technique, we investigate the spin-dependent transport through a closed Aharonov-Bohm interferometer coupled to ferromagnetic leads. With the Fano factor, We analyse the effect of the Fano and the Kondo resonance on the conductance and the variation of the conductance with the spin-polarization strength and the magnetic flux in both the parallel and the antiparallel lead-polarization alignments. Our results show that the conductance can be controlled effectively by the spin-polarization strength and the magnetic flux, while the line shapes of the conductance depend mainly on the magnetic flux and that a large tunneling magnetoresistance and a negative tunneling magnetoresistance can arise by adjusting the relative parameters. This system is a possible candidate for spin valve transistors and is of potential applications in the spintronics.

Based on both the cell equivalent circuit of cellular neural network and the electrical characteristic model of cellular neural networks（CNN） cell，the cell circuit of cellular neural networks is implemented. The activation function of cell circuit is made of two cascaded SET-MOS inverter, which is proposed previously by the author. The CNN cloning template is built by coupling capacitance of input terminal. Then the CNN and its application in image processing are built and studied. The computer simulation results show that the designed circuits is suitable for CNN implementation because of its simple structure, low power dissipation and fast response. The designed circuit can be used to form CNN of various scales so as to further satisfy the need of large-scale signal processing and improve the density of integrated circuit.

Vortex structures in high-temperature superconductors are studied by solving Bogoliubov-de Gennes equations based on a mean-field t-t′-U-V-V_{c} model. The results show that transition from checkerboard pattern to stripe structure for spin density wave, charge density wave, and d-wave orderings may occur by enhancing the strength of the on-site repulsion U. When a reasonable long-range Coulomb interaction is introduced into the model Hamiltonian, two-dimensional modulations or the checkerboard patterns may appear for the underdoped samples, which is consistent with the scanning-tunneling-microscopy experiments.

A linear phase high temperature superconducting （HTS） filter fabricated on LaAlO_{3} substrates is presented. The designed passband of the HTS filter is 10 MHz and the group delay ripples over 80% of the passband is less than 20 ns. The filter consists of novel resonators, which are able to minimize the spurious couplings between resonators. As a result, the filter shows not only the linear phase characteristic but also the symmetrical frequency response. The measured passband is 9.85 MHz. The return loss is better than 16 dB and the out-of -band rejection is better than 80 dB. The measured group delay ripples is about 20 ns, which is in good agreement with the simulated result.

The La_{0.7}Sr_{0.3}MnO_{3} sandwich structure separated by （La_{0.7}Sr_{0.3}MnO_{3}）_{m}（BiFeO_{3}）_{n} superlattices is grown in situ on SrTiO_{3}（001） substrates by RF magnetron sputtering. The X-ray diffraction scans indicate that the films are obviously superlattice structures. The resistivity-temperature curves measured in the case of current perpendicular to the plane geometry show that the films undergo metal-insulator transition at 290 K, which is a little lower than the temperature of single La_{0.7}Sr_{0.3}MnO_{3} film. When the current is within 0.01—10 mA, the peak resistivity of the （La_{0.7}Sr_{0.3}MnO_{3}）_{m}（BiFeO_{3}）_{n} films decreases with the increasing current.The change rate which is higher than that of single La_{0.7}Sr_{0.3}MnO_{3} film increases with the increasing thickness of the period films. The current-voltage curves indicate that the conduction mechanism in superlattices is space-charge-limited con-duction and a big bias voltage which is a characteristic of Schottky junction is also found in the current-voltage curves at low temperatures.

The magneto-mechanical coupling factor, electromechanical coupling factor, and magnetoelectric （ME） coupling factor of magnetostrictive/piezoelectric laminated composite, which are related to the geometric dimensions and the performance parameter of the magnetostrictive and piezoelectric materials, are analysed and derived. It is also demonstrated that the ME voltage coefficient at low frequency is directly proportional to the ME coupling factor while the ME voltage coefficient at resonance is directly proportional to the product of the ME coupling factor and the effective mechanical quality factor of the composite. In addition, the ME voltage coefficient is related to the intrinsic impedance of the composite. Multiple composites of distinct magnetostrictive materials （Terfenol-D, FeNi-based-alloy） and piezoelectric materials （PZT5-H, PZT8） are further analysed to demonstrate the theoretical analysis. The Terfenol-D/PZT5-H and FeNi-based-alloy/PZT8 laminated composites are fabricated and investigated, and the analysis gives better explanations to the experimental results.

By using electron spin resonance （ESR）, the intrinsic defects in high-quality semi-insulating 4H-SiC prepared by low pressure chemistry vapor deposition （LPCVD） are investigated. In dark-field condition, the results show that the defects have the characteristics of V_{C} and its complex compounds, while the absorption spectra are obviously asymmetry and have wider ESR half-width. The asymmetric chart and the wider ESR half-width are attributed to the higher testing temperature, non-homogeneous distribution of the defect concentration and the unsymmetrical crystal structure in 4H-SiC. The distributions of electrons have little effect on the ESR characteristic at the testing temperature of 110 K.

The dielectric properties of Ag/ZnO composite material are investigated and a strong low-frequency dispersion phenomenon is found. The experimental results are systematically studied in the frequency range of 0.1—10^{7} Hz and in the temperature range of 173—473 K. By means of normalization of conductivity, it is found that samples with different Ag contents show similar mechanism of dielectric loss, which is suggested as electron jumping between deep levels. In addition, it is also found that the dependence of E_{1mA} on Ag content is similar to that of α_{lf} on Ag content, which is a novel result in the research of varistor materials. The results can be fully understood by means of universal power law.

The temperature-dependence of dielectric-constant of BaTiO_{3} single crystals in 〈001〉 direction is measured under different voltages and frequencies. The crystal experiences rhombohedral-orthorhombic-tetragonal phase transition with the increase of temperature. Base on the assumption of dipoles rotation and the experimental results of dielectric constant, a model is proposed, which holds that the dipoles rotation path can be inferred by the dielectric properties of the adjacent structure phase of BaTiO_{3}. The dipoles rotation paths of rhombohedral, orthorhombic and tetragonal phases are given. The influences of bias dc electric field on the dipoles rotation path are discussed.

Based on the energy-level structure of quasi-three-level Yb ion, an amplified spontaneous emission（ASE） model in pumping process is set up. The stored energy density distribution and the energy that can be extracted in Yb:YAG crystal are calculated. The effect of ASE on energy-storage is investigated specifically, which includes the aperture, doping concentration and thickness, and working temperature of the gain medium. This paper gives an optimizing design of a pulsed energy-storage rep-rated Yb:YAG disk laser amplifier, which will be helpful in designing high-energy diode-pumped solid-state lasers based on Yb-doped materials.

Ge crystals doped in SiO_{2} glassy materials were formed by heating GeO_{2}/SiO_{2} glass at 700 ℃ in the presence of hydrogen. The GeO_{2}/SiO_{2} glass was prepared by the sol-gel technique. The Ge/SiO_{2} samples showed a special photoluminescence property to give off strong room temperature luminescence at 392 nm（3.12 eV）, secondary strong luminescence at 600 nm（2.05 eV）,and weak luminescence at 770 nm（1.60 eV）, when excited by 246nm （5.01 eV） ultra-violet light. The structure of this new luminescence material was studied by XRD, XPS, and TEM techniques. The results show that the existences of nanometer-sized （around 10 nm） Ge and GeO crystals in the SiO_{2} may cause the three band photoluminescence property. As a comparison, there is only GeO_{2} in SiO_{2} glass before the heating plus reducing process, and the photoluminescence property is not found.

The crystallization evolution of the nanostructured Si （ns-Si） in the Er-doped Si/Al_{2}O_{3} multilayer fabricated by using pulsed laser deposition technique and its effects on the Er^{3+} luminescence at 1.54 μm are investigated. Raman scattering and transmission electron microscopy measurements are used to characterize the microstructure evolution of the ns-Si during annealing treatment processes. The maximum photoluminescence intensity is obtained in the sample with ultrathin ns-Si sublayers annealed at 600—700 ℃, where the density, the size of Si nanocrystals, the interaction distance, and the optimized local environment for effectively activating the Er^{3+} are well controlled. From the analysis of the decay process of time-dependent luminescence, two decay channels are considered, the fast and slow decay channels. The bulk-like Si is responsible for the fast process and the Si nanocrystals are responsible for the slow decay process.

An antiferroelectric cathode material, lanthanum-doped lead zirconate stannate titanate （PLZST） located in the vicinity of antiferro-ferroelectric phase boundary, was prepared by solid state calcination method. The electron emission property of the novel antiferroelectric cathode under the negative triggering voltage pulses was investigated. The emission threshold value voltage from PLZST with 0.5 mm width under negative triggering pulses was 500 V. For negative triggering voltage of 500 V and extraction voltage of 3.5 kV, a large emission current of 690 A was obtained. It was indicated that the emission threshold value voltage was low and the emission current was large. Even when the triggering voltage was lower than the positive switch electric field, strong emission current can be obtained from PLZST. Finally, the mechanism of electron emission of PLZST under negative triggering pulses was discussed.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

A series of high rate growth μc-Si:H thin films with different thicknesses were deposited by very high frequency plasma enhanced chemical vapor deposition （VHF-PECVD） process with high power and high pressure. The microstructure of the μc-Si:H thin films was studied by the Raman and XRD spectra. It was found that the crystal fraction and grain size increased with the thickness of the thin film when the thickness was less than 1000 nm, and then came to saturation when the thickness was higher than 1000 nm. However, the performance of solar cells decreased obviously when the thickness increased from 1000 nm to 2000 nm. Considering the microstructure properties and the ion bombardment during the high rate process, we investigated the controlled microstructure evolution and the improved material quality by discharge power profiling, which improved the performance of solar cells. By optimizing the profiling parameters, such as the amount and the rate of change in discharge power, a high efficiency of 9.36% was obtained with an i-layer deposition rate of 1.2 nm/s. Furthermore, we used the improved μc-Si:H cell in an a-Si:H/μc-Si:H double-junction structure and achieved an initial active-area cell efficiency of 1114%.

AZO（ZnO:Al） polycrystalline thin films with strong adhesion to the substrate, as low as 89 Ω of sheet electronic resistivity and as high as 79% of visible light transmittance,are fabricated by PECVD （plasma enhanced chemical vapor deposition） method on glass and silicon substrate. The AZO film fabricated by PECVD is a useful attempt. The AZO transparent conductive film has the good photovoltaic properties like that of ITO （In_{2}O_{3}: Sn）; moreover, it is cheap, more nontoxic, and more stable in hydrogen plasma environment than ITO. The results obtained are very important to the selection of the technical conditions.

For modern processes at 90 nm and 65 nm technology nodes, the random yield loss can contribute much to the total yield loss. Hence, it is essential to calculate the critical area to analyse the areas of design, and make changes to improve the random yield. This study provides a novel weighted critical area （WCA） of arbitrary defect outline, which takes into account the clustering effect in the metal and empty regions of the chip as well as the size distribution of random defects. Then, two fast and accurate algorithms related-WCA extraction and its sort of WCAs are implemented, which can sever as a cost function of layout optimization for the random yield improvement.

Cd-doping Ba_{8}Ga_{16}Cd_{x}Ge_{30-x}（x=0.95, 1.00, 1.05, 1.10） type-I clathrates with different Cd contents were synthesized by combining solid-state reaction with spark plasma sintering （SPS） method. The effects of Cd doping on the structure and thermoelectric properties were investigated. Rietveld refinement reveals that Ba_{8}Ga_{16}Cd_{x}Ge_{30-x} compounds prepared by this method are type-I clathrates with space group pm3n; Cd atoms mainly occupy the 6c and 16i sites in the framework, and the atom displacement parameter （ADP） of Cd is relatively higher than that of other atoms. All specimens show the characteristics of p-type conduction. The carrier scattering mechanism is mainly ionized impurity mechanism in the low temperature range, and gradually changes to acoustical mechanism with the increase of temperature. With the increase of Cd content, the electrical conductivity increases while the Seebeck coefficient decreases gradually. The lattice thermal conductivity of the Ba_{8}Ga_{16}Cd_{x}Ge_{30-x} compounds is relatively low due to the larger ADP of Cd, and it decreases by about 38% compared with that of Ba_{8}Ga_{16}Ge_{30} The maximum ZT value of 0.173 is obtained at 600 K for Ba_{8}Ga_{16}Cd_{100}Ge_{2900} compound.

The effects of multiplicative noise on additive noise-induced internal signal stochastic resonance（ISR）are studied in a Neurospora circadian clock system driven by external signal or not. Two cases are investigated: multiplicative noise and additive noise are independent or correlated. The results show that in the two cases, there exists a critical intensity of multiplicative noise for the additive noise-induced ISR in the system without the external signal. When a multiplicative noise with intensity smaller than the critical level is introduced，the strength of ISR can be significantly reinforced; while the ISR behaviors cannot be further enhanced when the noise with the intensity larger than the critical level is introduced. The latter implies that the Neurospora system might be robust to environmental noise and sustain the intrinsic circadian rhythms. When the external signal is injected into the system, for the case of without correlation between two noises, there exists an optimal frequency （0003 Hz） of the signal for the ISR information amplification, but for the case of with correlation between the two noises, the ISR is suppressed by the signal with any frequency. In addition, the correlation’s intensity between the two noises can also control the ISR, and there exists a proper range of correlation’s intensity for the ISR amplification.

The electronic structure including some surface states of the 6[KF（]3[KF）]×6[KF（]3[KF）] R30° reconstructed 6H-SiC（0001） surface have been investigated by synchrotron radiation angle-resolved photoelectron spectroscopy （SRARPES）. The energy position of the bulk valence band maximum （VBM） is determined to be at （-2.1±0.1） eV related to the Fermi level by identifying bulk states from valence band spectra. The experimentally measured bulk energy band structure agrees well with the theoretical calculation result. Three surface states are clearly identified at the binding energies of -0.48 eV （S_{0}）, -1.62 eV （S_{1}） and -4.93 eV （S_{2}） referred to the Fermi level. The surface state dispersion is measured along ΓKM, the high symmetry lines of the surface Brillouin zone. Only surface state S_{0} （-0.48 eV） shows expected 6[KF（]3[KF）]×6[KF（]3[KF）] R30° periodicity in all probed SBZ. Surface state S_{0} should be attributed to the C—C dangling bonds of the surface reconstruction. Surface states S_{1} should be attributed to the unsaturated C dangling bonds.

The relative usage degree of the synonymous codon is computed and the use of preferences of the synonymous codon in 78 human genes（19967 codons） is analysed based on the quasi-amino acids coding. The results of Shi Xiufan et al. show that human genes clearly show the consistent preference in synonymous codon choice in all codon family based on the genomic genetic codes. That is, human genes prefer to use the codons with strong combination of the codon-anticodon， the codons ending with c, so that the use of the codons with moderate combination is avoided. The choice of codon in human genes is not only affected by the isochore and genome in the genome structure， but also related to the strength of combination with the codon-anticodon. All the above-mentioned factors affect the human genes，and so all the codon families clearly show the consistent preference to the synonymous codon. This study shows that the above-mentioned characteritics are more obvious when the method of quasi-amino acids coding is used.

We report a single molecule study on cisplatin-induced DNA compaction. It is found that, at a small external tension （<1 pN）, the DNA compaction time course is irregular with many continuous shortening processes and abrupt large size jumps. The time course becomes smooth and hyperbolic when the external tension increases to a moderate value, which is not large enough to inhibit the compaction. The time course depends on the external tension rather than the concentration of cisplatin; the latter only influences the compaction rate. The results are consistent with a looping-and-cross-linking compaction model. Namely, in aqueous solutions, cisplatin forms both monoadducts and diadducts with DNA. When cisplatin induces distant cross-links between DNA bases, micro-loops are formed, which make DNA compact. Further cross-linking between the micro-loops leads to complete compaction of DNA. In addition, the compacted DNA structure is quite stable.

Many systems in the real world can be described by evolving models of complex network, one of which is power system. Classical network models show great inconsistence with practical power grids. Based on the essential evolution characteristics of power grid, we propose a new local-world evolving network model for complex power grid, which exists in many physical complex networks. The statistical properties and dynamics of the proposed model are analytically studied. It is found that the degree distribution of this new model has a power-law tail, and its scaling exponent is between 3 and ∞. Numerical simulations for West American power grid and North China power grid and their comparison with random network and scale-free network indicate that the new evolving network model captures the essential features of real-world power grid. Furthermore, it is proved that power grid is neither a random network nor a scale-free network.

We present a process variations based stochastic collocation method to estimate interconnect delay. This method translates the strongly correlated process variations into orthogonal random variables by Cholesky decomposition. Polynomial chaos expression （PCE） and stochastic collocation method （SCM） are used to analyse the system response. A finite representation of interconnect delay is then obtained by using the collocation approach of minimizing the Hilbert space norm of the residual error. Experiment demonstrates that results obtained from the analysis method agree well with that from HSPICE simulation. The difference between the delays obtained from the analytical method and that from HSPICE is about 0.2% or less. Moreover, the method shows good computational efficiency, and much less running time has been observed compared with HSPICE simulation.

According to the comparability of the nonlinear terms and dispersion terms between the variable coefficient modified Korteweg-de Vries （VCmKdV） equation and constant coefficient KdV-mKdV equation, we transform properly the KdV-mKdV equation with known solutions, transplant its solutions to the VCmKdV equation with unknown solutions, and thus construct the transplantation relation between the solutions of two different equations. Utilizing this transplantation method of solutions, we obtain new exact solutions and solitary wave-like solutions of the coupled VCmKdV system, which is derived from a two-layer fluid model with source or sink. Then we compare the Bcklund transformation and this transplantation method, and analyse the influence of source and sink on the amplitude.

A kind of conserved quantity which is directly induced by Mei symmetry of Lagrange system is studied. The definition and criterion of Mei symmetry for Lagrange system are given. The condition under which Mei symmetry can lead to a conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the result.

The linear acceleration-dependent Lagrangians are studied. Under the symmetric conditions of coefficients in acceleration terms, the Lagrange's equations remain second-order differential equations. The approach to constructing an acceleration-dependent Lagrangian from its equations of motion is presented. The relations between the acceleration-dependent Lagrangians and the acceleration independent ones of the same system are studied. Two examples are given to illustrate the application of the results.

The Lie symmetry and Noether conserved quantity of discrete difference Hamilton system are investigated. Based on the extended mechanical variational principle of discrete time, the difference dynamical equations of Hamilton system are constructed. The invariance of difference equations of discrete system under infinitesimal transformation groups is defined to be Lie symmetry and the criterion for when discrete Noether conserved quantities may be obtained from Lie symmetries is also deduced. An example is discussed to show the applications of the results.

New exotic solitary wave and the painlevé integrability of one type of the nonlinear dispersive generalized DGH equation are studied. By Painlevé analysis, we discover that the nonlinear dispersive generalized DGH equation with m＝2 is integrable, which is a new integrable equation. By the new variable transformation and the auto-Backlund transformation，we obtain abundant exotic solitary wave solutions, such as compactons, peakons, new double solitary waves with peak points, and double solitary waves with blow-up points.

This study reports the transformations between the third-order Eulerian and Lagrangian solutions for the standing gravity waves on water of uniform depth. Regarding the motion of a marked fluid particle, the instantaneous velocity, the mass conservation and the free surface must be the same for either Eulerian or Lagrangian methods. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, we obtain the third-order asymptotic expressions for the Lagrangian particle trajectories and the period of particle motion directly in Lagrangian form. In particular, the Lagrangian mean level which differs from that in the Eulerian approach is also found as a part of the solutions. Therefore, the given Eulerian solutions can be transformed into the completely unknown Lagrangian solutions and the reversible process is also identified.

By considering the effect of two-dimensional uniform currents, a solution for linear surface capillary-gravity short-crested waves in water of finite depth is obtained. Both a generalized Doppler-shift relation and a generalized dispersion relation are first found, and the generalized intrinsic frequency with variety in dual values is directly correlated with the uniform currents.

The characteristics of spatiotemporal shaping and filtering of terahertz （THz） pulses passing through metal slits with finite thickness have been investigated by employing the finite-difference time-domain （FDTD） method. It is shown that this diffraction-based quasi-optical technique has a good influence on shaping and filtering of transverse magnetic（TM） polarized THz pulse, while has no effect on transverse electric（TE） polarized THz pulse. Furthermore, the numerical simulation results have been interpreted qualitatively by the planar waveguide theory and can be employed in the relevant experiments.

In virture of the eigenvalue equations of operators, the entangled states' completeness relation is proved from that of the coherent states, and the integral values of non-symmetric projective operators of entangled states are obtained.

An extended variational method for describing the dynamics of a Bose-Einstein condensate （BEC） chirped soliton in the presence of periodic and harmonic potentials is developed. It is shown that the BEC chirped soliton dynamics can be deduced via the extended variational method to a set of four coupled nonlinear differential equations. This deduced set of equations agrees remarkably well with full numerical simulations and highlights the dominant physical interactions in the system, namely amplitude, width, chirp, center-position, and center-frequency dynamics. The extended analytic theory provides a useful, accurate, and greatly simplified description of the governing BEC chirped soliton dynamics. It further gives the critical strength ratio of periodic to harmonic potential necessary to support multiple stable lattice sites for the BEC chirped soliton and demonstrates that the BEC chirped soliton can move selectively from one lattice site to another by simply manipulating the potentials. In addition, some interesting results for the experiments and applications of the BEC are also obtained.

Spin squeezing of two-component Bose-Einstein condensate, which is impacted by the periodic impulses, is investigated. The results show that spin squeezing can reveal the underlying chaotic and regular structures of phase space, namely, spin squeezing vanishes after a very short time for an initial coherent state centred in a chaotic region, but spin squeezing exists for a long time for an initial coherent state centred in a regular region. In particular, with time evolution, distribution and swing of the mean spin direction is closely related to the structure of the space where the initial coherent state centred in. Finally, spin squeezing dynamics of initial states centred in the whole phase space is investigated and a better quantum-classical correspondence is obtained.

Quantum communication is a process of quantum key distribution （QKD）. Current QKD technology restricts communication to a low bit rate. To improve the QKD bit rate and develop high rate and capacity, we propose a multiple-input-multiple-output quantum key distribution system. However, quantum field itself inevitably involves quantum noise （which is determined by the quantum mechanics ）, which restrains the increase of capacity, and limits space resource utilization, that is, the problem of spatial degrees of freedom arises. The quantumization of the photon field and the electromagnetic wave equation satisfying the Schrdinger equation condition are adopted to investigate the upper bound of the spatial degrees of freedom for MIMO quantum channels, which will provide theoretical support and technical basis for developing robust space time processing algorithm for MIMO quantum communication and designing high performance systems.

We investigate the influence of quantum noises on the processes of remote preparation of a qubit by using an Einstein-Podolsky-Rosen （EPR） state and a bipartite partially entangled state as the quantum channel respectively. By solving the master equation in the Lindblad form, we obtain the time evolution of the quantum channels. Then we use the trace distance to describe how close the output state and the initial state are in various noisy conditions. Our results show that the influence of the noise acting on z direction is the weakest, and the influence of the noises acting simultaneously on x, y, and z directions is the strongest.

We deduce a two-level model of light propagating in photonic lattices of Kerr medium and two kinds of saturated photorefractive medium,establish the classical Hamiltonian system, study the evolution of the phase-space motion of the Hamiltonian system for one kind of saturated photorefractive medium, namely, the Screening medium, and then study the nonlinear Landau-Zener tunneling numerically. Results show that the tunneling probability is enhanced when the nonlinearity is positive while it is restrained when the nonlinearity is negative.

Some fundamental social structures in human population, such as household, dormitory, and colleague, are of significant importance for epidemic spreading. In this paper, a growth model of scale-free network incorporating these local structures is introduced, in which both the node degree and the local structure degree follow a power-law distribution with the exponent depending on the size of the local structure. The existence of the local structures also results in the positive correlation between the nodes degree, which is a particularly key feature of social networks. By means of analysis and simulation, we study the effects of network structure on the SIS（susceptible-infected-susceptible） epidemic dynamics, and obtain the epidemic threshold and the phase diagram of prevalence, indicating that the propagation is coupled by the local infection process within local structure and the global infection process between local structures, both of which are governed by the network features and the transmission mechanism. These results are of scientific significance to the control of infectious diseases.

Cascading failures are common in real-life networks. To better explore the robustness against cascading failures on complex networks，by adopting the initial load of a node j to be L_{j}=k^{α}_{j}，where k_{j} is the degree of the node j，a new cascading model is proposed based on the local preferential redistribution rule of the broken node's load. According to a new measure to the robustness of a network，we further investigate cascading failures on four typical networks. The numerical simulations show that four networks reach the strongest robustness level against cascading failures and that the robustness against cascading failures on four networks has a negative correlation with the average degree 〈k〉 when α=1. The simulation results are also verified by the theoretical analysis.

The influences of a kind of non-periodic force，modeled by bounded noise or chaotic driving，on chaos control of nonlinear dynamical system are studied. Suppressing chaos as well as inducing chaos in a periodically driven Duffing-van der Pol oscillator with 5 nonlinear components is studied in detail. By examining the separation distance，the largest Lyapunov exponent，the scaling exponent of power spectrum, and the Poincar map of the considered oscillator，it is found that the non-periodic driving of appropriate amplitude，on one hand，can eliminate the sensitive dependence on initial conditions，then suppress the chaotic behavior and convert a chaotic attractor to a strange but nonchaotic one in this DVP oscillator. On the other hand，it can induce the chaotic behavior and then convert a periodic attractor to a chaotic one as well. Thus，the dual roles of non-periodic driving，i.e. suppressing and inducing chaos，in chaos control of nonlinear dynamical systems are revealed.

Based on the principle of directing chaotic orbits, the method of directing orbits is proposed using particle swarm algorithms in chaotic control. After the orbits reach the target region, OGY method is then used to make the chaotic systems stabilized to the fixed point. The simulation of Hénon chaotic system indicates that the new method realises better chaotic control.

It is easy to construct a hyperchaotic system，and many systematic approaches，based on Chua system，can be used for generating multi-scroll attractors. However, few reports discuss the smooth Lorenz-like system with multi-wing attractors，and the attractors with both hyperchaotic dynamics and multi-wing topological structure are seldom reported. Based on the existing smooth hyperchaotic system，the common characteristics of these systems are analyzed. A novel coordination transformation method is used for converting all the attractors' topological structure from two-wing to four-wing. Moreover，the hyperchaotic property is preserved in resulting system，the complexity of attractors is enhanced，and they are more suitable to be used in secure encryption communication.

The largest Lyapunov prediction method for dealing with the end issue of empirical mode decomposition （EMD） is proposed. Generally，the largest Lyapunov prediction method extends the time series near both ends of the data. After the extension，the spline does not swing at both ends of the data. Because the intrinsic characteristics of the signal are considered, the end issue becomes more reasonable. The simulation results proved that the new method can be used to solve the end issue effectively.

For the projective synchronization of fractional-order chaotic systems，a controller based on active sliding mode theory is presented. Based on the stability theory of fractional-order linear system，stability of the proposed method is analysed. Two cases of projective synchronization，i.e.identical fractional-order Liu-Liu systems and different fractional-order Chen-Liu systems，are implemented separately. The simulation results show the effectiveness of the proposed controller.

A kind of generalized predictive control fast algorithm with constraint matrix for Hénon chaotic system is proposed. We firstly identify the chaotic system by recursive least squares parameter of forget factor, and then add one kind of constraint matrix to this algorithm. The introduction of the constraint matrix avoids the matrix inversion computation. The method needs smaller computer memory and the computational speed is higher. The abilities of tracking the reference signal and restraining the parameter perturbation and stochastic disturbance are improved. The simulated results show the effectiveness of this algorithm.

A nonlinear controller is proposed to acquire generalised projective synchronization and arbitrary trajectories of full states of a fifth-order hyperchaotic circuit system. By adjusting the scaling factor and the accelerated factor, generalized projective synchronization between the fifth-order hyperchaotic circuit system and the hyperchaotic systems,chaotic systems and periodic signal can be rapidly realised, and the fifth-order circuit's hyperchaotic circuit system can also be driven to arbitrary periodic orbits or fixed point rapidly. Simulation results are presented to demonstrate the effectiveness of the proposed method.

For two linearly bidirectional coupled unified chaotic systems，based on adaptive control technique, the anti-synchronization is completely realised. The adaptive-controller and the coupling coefficient are both estimated by the Lyapunov stable theorem and the minimum value theorem. This method can realise anti-synchronization, not requiring to know the scope of the coupling coefficient and the maximum value of the coupling chaotic systems. We apply this criterion to the case of the coupled Chen-Chen system to test our method，the numerical simulations illustrate that this method has a good performance.

Passive walking model can exhibit natural gait on a slope， depending only on the gravity. The gait changes with the changing of parameters. The fixed point of the periodical gait can be obtained by the combination of cell mapping method and Newton-Raphson iteration. By the aid of cell mapping method，periodical cells can be used as the initial value of iteration，and the basins of attraction can be obtained. Simulations of models with different parameters show that the increasing of moment of inertia will result in the appearance of period-doubling and chaotic gaits. The same effect can be obtained by the decreasing of foot radius or position of center of mass.

The projective synchronization problems of uncertain hyperchaotic systems is investigated. Based on the Takagi-Sugeno （T-S） fuzzy model，an adaptive controller and the parameter update rule are designed. The feasibility of the proposed scheme is verified according to Lyapunov stability theory. Using the designed controller，parameters identification and the projective synchronization of uncertain hyperchaotic systems can be achieved simultaneously. Hyperchaotic Lorenz system is employed to illustrate the effectiveness of the proposed scheme.

Based on the definition of monopolized sphere，instantaneous chaometry and k step chaometry are defined，which are the stable characteristic of chaotic orbit. Uniform index is defined by monopolized sphere，and its description of uniformity is quite consistent with peoples understanding. The contained uniform index，which is a transitionary concept，is similar to uniform index and has good mathematical property. For random orbit，the contained uniform index converges to 1/V_{n}（1）（V_{n}（1） is the volume of the sphere with radius 1），when the point number of an orbit is great enough，uniform index is approximately equal to the contained uniform index. Only by properly selecting the polyhedron containing the basin of attraction of a discrete dynamic system，the ratio of instantaneous chaometry and uniform index is constant. The application of uniform index on Logistic map shows that as the parameter of Logistic map r increases, the orbits are more and more uniform but the expectation uniform index will be less than 0.5，which is that of random orbit，so asymptotical periodic orbit and random pattern are the two extreme status of chaotic orbits.

Wavelength division multiplexing transmission of chaotic optical communication and current optical communication is numerically confirmed and analysed. For a 100 GHz channel span，a 1-Gbit/s digital message extraction is achieved in chaotic optical communication system and a 2.5-Gbit/s digital signal is received in current optical communication system. The results show that when the peak power of digital signal in current optical communication is less than 17 dBm，chaotic optical communication can realise parallel transmission of 80 km. In addition，when the peak power of digital signal in current optical communication is 7 dBm，the quality of the received signal in current optical communication is hardly interfered by signals of chaotic optical communication. As the transmission distance increases from 80 km to 160 km，the opening of the corresponding eye diagram decreases from 82% to 70%.

Most nonlinear dynamic systems may exhibit a certain symmetrical form. Symmetry is a kind of invariance，maybe appearing in different topological forms under different situations，but always keeping the characteristic of symmetry. The transition between different symmetric forms often leads to symmetry breaking bifurcation or crisis. Many studies on symmetry breaking bifurcations of phase trajectories of a nonlinear dynamical system have been reported，most of which are related to periodic or quasi-periodic orbits. Only a few of them ever mentioned that “duality” might also exist for a couple of chaotic attractors in symmetrical nonlinear dynamical systems. Recently，in the study of the saddle-node bifurcation resulting from symmetry breaking of periodic phase orbits in a Duffing oscillator driven by a sinusoidal excitation，an interesting phase portrait of the flow pattern of discrete Poincaré mapping points has been obtained after symmetry breaking bifurcation. Along with the flow pattern，two stable periodic nodes and one periodic saddle，together with its stable and unstable manifolds，are shown，which are all in a regular form yet. In this study, as an extension of the above results，a complicated portrait for attractive basins of coexisting periodic and chaotic attractors in a parametrically driven double-well Duffing system is obtained，which is fractal，interwoven，yet symmetrical. In addition，the neighboring symmetry breaking crises are studied qualitatively.

The new two mode coherent entangled state representation 1p,β〉 is proposed by the technique of integration within an ordered product of operators. Its characteristics and mechanism are analysed. The results show that, the common eigenvector |p,β〉 of p_{1}-p_{2} and a_{1}+a_{2} exhibits both the characteristics of the coherent state and entangled state. The 1|p,β〉 makes up a new quantum mechanical representation and possesses the completeness relation. The ideal single-mode squeezed state |p=0〉_{2}=exp［1/2a^{+2}_{2}|0〉_{2} and the vacuum state |0〉_{1} overlapping on a beam splitter may produce the coherent entangled state |p,β〉at the output by the modulation of the laser field.

Er^{3+} doped and Er^{3+}/Yb^{3+} co-doped superfine LaF_{3} powders are prepared using co-precipitation method. The sample shows spherical particles with size of about 250 nm. The quantum efficiencies of ^{4}S_{3/2} and ^{4}F_{9/2} levels in the prepared Er^{3+} doped LaF_{3} powders are calculated to be 67.0% and 71.9%, respectively. With the enhancement of the Yb^{3+} doping concentration, The upconvertion intensity increases as a function of excitation power more slowly due to the enhancement of the sensitization of Yb^{3+} to Er^{3+}. The Er^{3+}-Er^{3+} interaction is also reinforced as the Yb^{3+} concentration increases. This leads to the increase of the ratio of the green emission to the red one with the enhancement of Yb^{3+} concentration.

The measurement sensitivity can be greatly improved when tunable laser spectroscopy together with the method of wavelength modulation of second harmonic detection is used to measure the gas density. However, light transfer and circuit delay will lead to unknown phase delay. The measurement results of second harmonic signal will be seriously influenced by the phase change of the frequency-doubled reference signal relative to the measured signals containing information of gas density. A four-channel multiplier demodulation circuit is designed here. Sinusoidal signals and cosine signals are used to demodulate measured signals. Then two demodulated signals appear relating to the phase difference of sinusoidal value and cosine values after the measured signals pass the integral circuit. The amplitude signals can be obtained, which have no relation with the phase difference when demodulated signals are squared through the adder and the phase difference is eliminated. Experiment shows that the stability of the measured results in the system has been improved greatly if the obtained second harmonic signal keeps stable when the phases change from 0° to 90°.

Close-coupling method was applied to the ^{3}He（^{4}He,^{5}He）-H_{2} system, and the second vibrational excitation cross sections of “00-20，00-22，00-24，00-26” at different incident energies have been calculated．By analysing the differences of these partial wave cross sections, the change rules of how the partial wave cross sections change with the mass of isotope atom and the relative kinetic energy of incident atoms are obtained.

Size modification of Au nanoparticles （NPs）, deposited on the Au-thick film surface, induced by highly charged ions （HCI） ^{40}Ar^{12+} with fixed low dose （4.3×10^{11} ions/cm^{2}） but various energyies （ranged from 146.64keV to 290.64keV） at room temperature （293.15K）, was investigated by atomic force microscopy （AFM） and transmission electron microscopy （TEM）. The selected ^{40}Ar^{12+} beams were provided by electron cyclotron resonance source （ECRIS） of the National Laboratory of the Heavy Ion Research Facility in Lanzhou （HIRFL）. The morphological changes of NPs were interpreted by collisional mixing model, Ostwald ripening （OR） model and inverse Ostwald ripening （IOR） model of spherical NPs on a substrate. Theoretical and experimental studies both prove that there exist the critical energy E^{*}, for low ion energy （E<E^{*}）, the mean diameter R of NPs increases with the increasing energy of incident ions E, while for higher projectile energy （E>E^{*}）, it decreases with increasing energy.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Flow field induced by the plasma actuator in quiescent air was measured by particle image velocimetry system. Boundary layer flow control in flat plate by the plasma actuator was investigated experimentally. Experimental results showed that the relation between exciting voltage and induced velocity magnitude was linear, but the influence of supply frequency was not evident. Mechanisms of plasma flow control were preliminarily ascertained to be results of collisions and temperature increase. Numerical simulation results showed that the thermal effect of the plasma was evident without incoming velocity. Methods of increasing plasma actuator's intensity were introduced briefly.

High quality interference pattern was obtained with a modified Mach-Zehnder interferomenter. An FFT analysis is applied to extracting the phase of the reconstructed interferograms, and then the inverse Abel transformation is used to calculate the three-dimensional electron density distribution. The electron density and the plasma expanding velocity at various delay times were obtained. The results show that the formation of the plasma channel in the early stage of the laser induces air plasma, and the rapid decrease of the plasma expanding velocity accelerates the collapse of the plasma channel. At about 48 nanosecond time, the eccentricity of the plasma shape reaches the maximum value and then evolves to a circular shape.

Base on physical amplification models established to describe the broadband laser pulse amplification processes, using numerical simulation methods, we analyse the amplification abilities of the Nd:glass laser system under different spectral linewidths. The results indicate that the output energies decrease with the increasing spectral linewidth. Compared with narrowband laser pulse of 3000 J/1ns, under the same conditions, the output energies of broadband laser pulse will reduce 2%, 11% and 27% for 2nm, 5nm and 10nm laser pulses,respectively. The influences of cross relaxation on the amplification processes are also studied. The output energies of completely nonhomogeneous broadening will reduce about 20% compared with that of completely homogeneous broadening. Then, the range of cross relaxation time is estimated to be 0—10 ns.

We study the formation mechanism of the double piral arms in vortex with the eddy equation in column coordinates. Results show that growth of undulations is very quick when m=2（double spiral arms） in basic flow field,whereas the increment rate is limited over time. Undulations can evolve into double piral arms and expand toward outside. Mechanism of undulation development is the strong advection process in which vorticity is transfered from basic to undulation field.

The diurnal variation of the tropical convection is investigated using hourly outputs from a two-dimensional cloud-resolving model simulation. The features of cloud microphysics in tropical convections are proposed by the contrastive analysis of the simulation. The model is forced by the observational data obtained from tropical ocean global atmosphere coupled ocean-atmosphere response experiment as the initial and boundary fields. The diurnal composites are carried out in weak diurnal SST variations （case W） and strong diurnal SST signals （case S） according to the amplitude of diurnal SST variations. The simulation results show that the ice water path in case W is larger than the liquid water path in case S, and more water cloud and less ice cloud exist in case W than in case S. The results also show that the surface rain rates reach their peaks in the early afternoon in case S, while the surface rain rates reach their peaks in the night in case W. Further comparison of cloud microphysics budgets shows that the coagulation of precipitation ice （sum of snow and graupel） is less than the coagulation of liquid water （sum of cloud water and precipitation water） and ice cloud can be formed in case W.

The five-parameter model is proposed and the parabolic equation numerical model of electromagnetic waves propagation is used to calculate the propagation loss of electromagnetic waves, then GA （genetic algorithm） is used to retrieve the duct parameter and the parameter of GA are discussed. The ability of restraining noise of retrieval algorithm is tested. Experimental results show that when the observation errors are less than 10%, the retrieval precise is credible, but when the observation errors are larger than 10%, the retrieval precise is bad. These results can provide useful information to practice inversion and radar designing.

Using the Bayesian-Markov chain Monte Carlo （MCMC） method, based on the measurement information of radar clutter（electromagnetic propagation loss）,we obtain the posterior probability density of the duct parameter by describing the prior information of the duct parameter as the prior probability density. And then, Gibbs sampler of the MCMC method is used to sample the posterior probability density. The sample maximal likelihood is regarded as an evaluation of the duct parameter distribution. The results of simulation experiment show that this set of methods make good use of the prior information and the inversion precise is better than the genetic algorithm. In addition, it is capable of describing （definite or indefinite） prior information in a convenient and controllable way, as well as capable of giving the complete solutions, which is very important to practical applications.

Based on recent studies of nonlinear science, we reconstruct dynamics of National Centre of Environment Prediction （NCEP） daily temperature series from 1948 to 2005 of grids located in China with the time-delay method and then analyse the dynamics structure by using dynamical correlation factor exponent Q.Eight significant temperature change regions are obtained. The characteristics of temperature changes and frequencies of extreme temperature in these regions are discussed, and the probable correlations between temperature changes and frequencies of extreme temperature are studied. Results indicate that, 1） the temperature and frequencies of extreme high temperature in ZhunGe’Er and North China both increased during the past 58 years, while frequencies of extreme low temperature in South China decreased. Furthermore, north oscillation, south oscillation, North Pacific oscillation and El Nio-south oscillation have distinct influence on temperature changes in North China, North-East China, west of West-South China and east of West-South China, while El Nio has distinct influence on South China and South East China. 2） The reason for warming during the past 58 years might be the increase of frequencies of extreme high temperature and the decrease of frequencies of extreme low temperature. 3） The abrupt change of extreme high/low temperature in the 1970s is 3—4 years later than that of abrupt temperature change. That is to say, the process of abrupt temperature change might be the inter-grade of extreme temperature from one stationary period to another stationary one.

The occurrence of record breaking temperature events （RBTE） became more and more frequent under the background of global warming. What is the probability that the current temperature record will be broken in the next five years? In this study, answers are provided by given a variety of simple statistical models for temperature, and the relationship between the probability of RBTE of China and the global warming is explored by comparative analysis of the probability of RBTE in the last 50 years. The results show that the frequency of RBTE is influenced by global warming and the autocorrelation. This study quantitatively estimates the relationship between the probability of RBTE and global warming, which can deepen our knowledge about the in-creasing frequency and amplitude of RBTE under the background of global warming.

According to the occurrence and maintenance of torrential rain relating closely to moisture convergence increment in low layer of troposphere, factors affecting the evolution of divergence is analysed to reveal the dynamic mechanism of heavy rainfall maintenance. Starting from the primitive equations, we obtain a new type of divergence equation including the coupling forces between Q vector and vertical shear of wind. Analysis on this equation brings to light the main factors to influence the evolution of divergence. They are separately the barotropic non-equilibrium force and the baroclinic coupling forces between Q vector and vertical shear of wind. Especially, the evolution of divergence is only controlled by the above-mentioned two factors on the layer with the maximum convergence . In addition, the definite integral for new type of divergence equation is formed from the earth’s surface to the un-divergent level. Results show that the self-exciting process of divergence fields lead to the decrease of convergence in the low layer of troposphere. Oppositely, the barotropic non-equilibrium force and the baroclinic coupling forces between Q vector and vertical shear of wind are the main factors that promote the increment of convergence in the air column, which we should pay more attention to in studying the mechanism of heavy rainfall maintenance.