In this paper, we introduce a further generalized projective Riccati equation method and apply it to solve the (2+1)-dimensional modified dispersive water-wave system. Many new types of non-travelling wave solutions are obtained for this system.

This work reveals a novel phenomenon—that the localized coherent structures of a (2+1)-dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2+1)-dimensional higher-order Broer－Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.

In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing－Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point (x,\dot{x}) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio α.

The synchronizing problem of a chaotic system is investigated based on the observer design. The nonlinear section is assumed to satisfy the Lipschitz condition. Firstly, the normal observer is designed based on the known Lipschitz constant and the results are given in linear matrix inequality (LMI) form. Then a fairly simple adaptive observer is designed with the Lipschitz constant unknown. Simulations on synchronizing the Lorenz system are investigated and the results show the validity and feasibility of our main results.

The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.

In this paper, some key techniques of KTiOPO_4 optical parametric oscillation (OPO) laser with repetitive frequencies and twin wavelengths output have been analysed theoretically and studied experimentally in detail. An intracavity optical parametric oscillator (IOPO) has been applied. Operating under 20Hz, laser output energy of more than 38mJ with twin wavelengths 1.57μm and 1.06μm has been achieved. Results of the experiments agree well with the theoretical discussion.

In order to optimize the axial irradiation uniformity of a laser in plasma, this paper investigates the role played by the compound lens using a ray-tracing method. Obtained results show that the adoption of the compound lens is capable of increasing the axial line-focus length. Meanwhile, after the energy attenuation in the plasma has been considered, moderating the optical parameter of the compound lens to obtain the corresponding energy output to compensate for the attenuation optimizes the irradiation uniformity along the focal line.

An important issue in developing applications for photopolymers in holography is the effect of shrinkage on recording properties. In this paper, we introduce a model to describe real-time formation of a single grating in photopolymers at any geometrical angle, under the assumption that the shrinkage is in proportion to the polymerization. This model combines polymerization kinetics with the coupled-wave theory, explaining the shrinkage effect on the diffraction efficiency. The model is validated by comparing its predictions with the experimental results for a film of 99μm thickness.

The atomic dynamical properties in the system with competing k-photon and l-photon transitions are studied fully by means of quantum theory. We discuss the influences of the mode－mode competition, the relative competing strengths of the atom and the two-mode field, and the initial state of the system on the atomic dynamics. We show that the presence of the mode－mode competition can result in quite a periodical collapses-revivals of the atomic inversion and the increase of the initial photons of the system can lead to the collapse－revival phenomenon and prolong the revival time of the atomic inversion.

We present an efficient scheme for preparation of the multi-atom W state via cavity quantum electrodynamics. Involved in this scheme are n identical two-level atoms and a single-mode cavity field. Discussion indicates that this scheme can be realized easily by current technologies.

The population transfer in effective three-state systems driven by laser beams has been studied based on the theory of Lewis－Riesenfeld Hermitian invariants in the full- and partial-adiabatic approximations. A strict formulation of adiabatic conditions is given, and a new adiabatic condition for inducing a complete population transfer is found.

Correlated perturbations are considered in a dark soliton system, and their effects on soliton propagation and interaction are investigated numerically. These perturbations result in large sidebands, lead to submergence of dark soliton, and enhance the interaction. The correlation amplifies these effects and shortens the distance until submergence. The comparison of the distinction is made between the degradations of these effects on dark soliton and the corresponding bright soliton. It is found that these effects on dark soliton are less than those on bright soliton. Finally the nonlinear gain is introduced to suppress efficiently these effects.

A distributed feedback Ti:sapphire laser (DFTL) pumped by a 532nm Q-switched pulse is proposed for the generation of tunable picosecond pulses. With coupled rate equation model, the temporal characteristics of DFTL are obtained. The numerical solutions show that the DFTL pulse with a 50-ps pulse duration and as much as 3.5mJ pulse energy can be obtained under 40-mJ, 5-ns pulse pumping. The dependence of output pulse width on the laser crystal's length, pumping pulse duration, and pumping rate is also discussed in detail.

In this paper, amplified double Rayleigh backscattering noise (DRB) in the optical fibre Raman amplifier is analysed. Expressions are presented for both forward pumping and backward pumping schemes. Calculation is performed to show the effective suppression of DRB noise by employing an optical isolator. The optimal position for the isolator is determined and is found to be insensitive to the power levels of the signals and pumps. The results show that a reduction of the DRB noise by almost 2 to 3 orders can be reached.

In this paper, the enhancement of light-induced scattering in congruent SBN:Cr (Sr_{0.61}Ba_{0.39}Nb_2O_6:Cr) crystals in the presence of an externally applied electric field and its suppression are studied. If a coherent image is focalized in SBN:Cr crystal without applying external electric field, the output image will remain clear, because of the weak photorefractive effect in the crystal. When a field is applied properly along the crystal axis, markedly enhanced scattering from the signal beam and the output image dispersion can be observed due to the increase of the photorefractive two-beam coupling gain and the light-induced index change in SBN:Cr crystals. By introducing a coherent or incoherent beam with higher intensity the light-induced scattering can be suppressed through the erasure of scattering gratings. The difference between coherent and incoherent beam is that the former can also amplify the signal beam as the scattered light is removed, whereas the latter can only make the signal beam revert to its initial state. The results obtained under different experimental conditions are consistent with theoretical analysis.

The basic optical property and phase-matching of new mixed AgGaGeS_4 crystal are presented. Frequency conversion, in particular the SHG of 30ns pulses of 9μm emission band of transversely excited atmospheric-pressure (TEA) CO_2 laser, is realized in AgGaGeS_4 for the first time. As high as 0.57% peak power and 0.3% external energy efficiencies, and 0.7mJ harmonic pulse energy are obtained for the 9.55μm emission line at pump intensity of 4% level of the damage threshold.

We propose a ring photonic crystal working in the near infrared region, where the air holes in the background material GaAs are arranged to form a series of rings. We find that the band gaps do not depend on the incident direction, and only a small number of rows are needed to create a frequency gap in the transmission spectrum. The transmission spectra of both P and S polarizations show that there is a complete bandgap in the hexagonal ring photonic crystals and the ratio of gap width to mid-gap frequency is as high as 11%.

The entanglement properties are investigated based on linear entropy, and nonclassicalities are examined of output fields from a beam splitter for pure binomial state inputs. It is shown that the properties of the entanglement and the photon statistics of output fields are not only strongly dependent on the parameters of input binomial states but also quite involved with the nature of the beam splitter. The best entanglement can be obtained when the parameters of both input states and the beam splitter are chosen appropriately. Finally, we analyse briefly the distinguishability between the joint input state and the joint output state.

In this article based on the spectral phase interferometry for direct electric-field reconstruction (SPIDER), the femtosecond pulses with various phase characters are numerically simulated. The spectral phases and amplitudes of the transform-limited pulse, the linear chirped pulse, the cubic dispersion pulse, the quartic dispersion pulse, the self-phase modulation pulse and the pulses with the combination of different chirped characters are retrieved. These characterized pulses are applicable to the real-time measurement as samples for diagnosing the chirped characters of pulses quickly.

Based on a full-vector model, a theoretical study on a kind of high birefringence photonic crystal fibre is presented. Due to introducing air holes of two different sizes into the cladding, twofold rotational symmetry was obtained. We demonstrate the possibility of achieving high birefringence that is at least one order of magnitude higher than that of conventional polarization-maintaining fibres. The dependences of modal birefringence, modal field and differential group delay on the structure parameter of the fibres are discussed in detail. The numerical results are in very good agreement with the experimental results in the literature.

In this paper, the probe absorption spectrum of an atom in a double-band photonic crystal have been studied. In the modes, we assume that one of the two atomic transitions in a Λ-type atomic system is interacting with free vacuum modes, and another transition is interacting with free vacuum modes, isotropic photonic band gap (PBG) modes and anisotropic PBG modes, separately. The effects of the fine structure of the atomic lower levels on the probe absorption spectrum are investigated in detail in the three cases. The most interesting thing is that the two (four) transparencies at one (two) probe absorption peak(s), caused by the fine structure of the lower levels of an atom, are predicted in the case of isotropic PBG modes.

The sub-Doppler transmission spectrum in a thin vapour layer (about 150 μm) was observed at room temperature using the wavelength modulation technology. The absorption signal and its second-order harmonic were detected with an external-cavity diode laser. A sub-Doppler spectrum corresponding to resonant transitions of the caesium D_2 line (6S_{1/2}→6P_{3/2}) was demonstrated. The dependence of the transmission signal on the intensity of the laser was also investigated.

Considering the overlapping among atoms in the molecule and the not full transparency of the molecule by electron, we propose a new formulation of the additivity rule (AR). Here the new AR is employed to calculate the total cross sections (TCS) for electron scattering on hydrocarbon molecules C_2H_2, C_2H_4, C_2H_6, and C_3H_8 over an incident energy range of 10－2000eV. The results are compared with the experimental data and other available theoretical calculations. This gives good agreement.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The evolution of a local helical perturbation and its stability property for arbitrary magnetic shear configurations are investigated for the case of in cylindrical geometry. An analytic stability criterion has been obtained which predicts that a strong magnetic shear will enhance the instability in the positive shear region but enhance the stability in the negative shear region. The perturbations with the poloidal and toroidal perturbation mode numbers m/n=1/1 is most unstable due to the stabilizing terms increasing with m. For m/n=1/1 local perturbations in the conventional positive magnetic shear (PMS) configurations, a larger q_{min} exhibits a weaker shear in the core and is favourable to the stability, while in the reversed magnetic shear (RMS) configurations, a larger q_0 corresponds to a stronger positive shear in the middle region, which enhances the instability. No instabilities are found for m≥2 local perturbations. The stability for RMS configuration is not better than that for PMS configuration.

The cross-field diffusion coefficient (D_⊥) at the edge in the HT-7 tokamak is close to the Bohm value when the line average electron density ranges from 1.5×10^{19} to 3.0×10^{19}m^{-3}. The energy profile of the particles is derived directly from the H_α(D_α) line shape; the dissociative excitation of molecules is dominating when the local electron temperature is above 10eV. By means of the Monte Carlo method the D_α line shape is also simulated. We find that the molecular dissociation contributes to 57% of neutral atoms and 53% of emission intensity in front of the limiter, and 85% of neutral atoms and 82% of emission intensity in front of the wall. The influence of atomic and molecular processes on the energy balance is discussed for the scrape-off layer (SOL), and the power loss from molecular dissociation is found to be 6×10^4kW at the SOL. The ion Bernstein wave (IBW) can effectively suppress the magnetohydrodynamic behaviour, the fluctuation levels and the turbulence; the D_⊥ in front of the limiter declines from 0.84 to 0.2m^2·s^{-1} and the particle confinement time rises from 9 to 12ms.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Nanocrystalline tungsten trioxide particles were prepared by a wet-chemical method. Transmission electron microscope (TEM) analysis shows that the average grain size is about 15nm. The oxygen deficiency of nanometre-sized sample is higher than that of ordinary tungsten trioxide. The electric conductivity increases because of high oxygen deficiency. Ironic relaxation polarization and crystallographic shear (CS) planes theory were used to explain the unusual dielectric characteristic of nanocrystalline tungsten trioxide.

The dynamic evolution of the lamellar eutectic of binary alloys in directional solidification is studied in detail using the Monte Carlo technique. The simulated results can be summarized into two aspects: ({1}) the lamellar spacing λ is found to be inversely proportional to the chemical potential difference Δμ, predicting a linear relationship between the kinetic supercooling ΔT_k and total supercooling at the solid/liquid (S/L) interface; (2) as the solidifying velocity R is low, the dynamic product λ^{2}R shows a considerable dependence on temperature gradient G_T in the liquid in front of the S/L interface, although this dependence becomes much weaker at a high R.

Based on a force constant model, we investigated the phonon spectrum and then specific heat of single-walled boron nitride nanotubes. The results show that the frequencies of Raman and infrared active modes decrease with increasing diameter in the low frequency, which is consistent with the results calculated by density functional theory. The fitting formulae for diameter and chirality dependence of specific heat at 300K are given.

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

We study theoretically the low-temperature electronic transport property of a straight quantum wire under the irradiation of a finite-range transversely polarized external terahertz (THz) electromagnetic (EM) field. Using the free-electron model and the scattering matrix approach, we show an unusual behaviour of the electronic transmission of this system. A sharp step-structure appears in the electronic transmission probability as the EM field strength increases to a threshold value when a coherent EM field is applied. We demonstrate that this effect physically comes from the inelastic scattering of electrons with lateral photons through intersubband transitions.

By developing the recursive Green function method, the transport properties through a quantum wire embedding a finite-length saw-tooth superlattice are studied in the presence of magnetic field. The effects of magnetic modulation and the geometric structures of the superlattice on transmission coefficient are discussed. It is shown that resonant peak splitting of this kind of structure is different from that of ‘magnetic' and ‘electric' superlattices in two-dimensional electron gas. The transmission spectrum can be tailored to match requirements through adjusting the size of saw-tooth quantum dot and field strength.

By the numerical method, we show a transition process from static to dynamic electric-field domain formation in semiconductor superlattices. During this transition, there can be noticed a sawtooth-like zone in which static and dynamic electric-field domain zones appear alternatively with increasing voltage. Therefore, a dynamic dc voltage band emerges from each sawtooth-like branch of the current－voltage characteristic. These results are qualitatively in agreement with experiment.

The random matrices theory is applied to a study of the heat capacity of small metallic grains. The numerical calculations indicate that the level distribution and the difference between the particles respectively with an even and an odd numbers of electrons are important for the heat capacity of the small metallic grains at a low temperature and the level correlation mainly affects the heat capacity at a high temperature.

Microfabrication and the magneto-transport characteristics of the magnetic tunnel junctions (MTJs) with a spin-valve-type structure of Ta (5nm)/Ni_{79}Fe_{21} (25nm)/Ir_{22}Mn_{78} (12nm)/Co_{75}Fe_{25} (4nm)/Al(0.8nm) oxide/Co_{75}Fe_{25} (4nm)/Ni_{79}Fe_{21} (20nm)/Ta(5nm) were investigated in this paper. A series of experimental data measured with a MTJ was used to verify a magnon-assisted tunnelling model and theory. Furthermore, a micromagnetics simulation shows that the butterfly-like vortex domain structures can be formed under a current-induced Oersted field, which decreases the net magnetization values of the ferromagnetic electrodes under a large dc current (i.e., in high voltage regimes). It is one of the main reasons for the tunnel magnetoresistance ratios to decrease significantly at high voltage biasing.

Resonant tunnelling diodes with different structures were grown. Their photoluminescence spectra were investigated. By contrast, the luminescence in the quantum well is separated from that of other epilayers. The result is obtained that the exciton of the luminescence in the quantum well is partly come from the cap layer in the experiment. So the photoluminescence spectrum is closely related to the electron transport in the resonant tunnelling diode structure. This offers a method by which the important performance of resonant tunnelling diode could be forecast by analysing the integrated photoluminescence intensities.

Femtosecond laser-induced dissociation and Coulomb explosion of polyatomic molecule C_2H_6 were systematically investigated using a time-of-flight mass spectrometer and a chirped pulse amplifier laser. With the laser intensity varying from 2.4×10^{15}W/cm^{2} to 1.2×10^{16}W/cm^2, strong molecular ions C_2H_n^+ (n=0－6) and atomic ions C^{m+} (m=1－3) signals were observed. The double-peak structure of atomic ions indicated the occurrence of Coulomb explosion. Compared with the nearly isotropic distribution of C^{+}, highly charged ions C^{m+} (m=2－3) exhibited a sharply anisotropic angular distribution, which was attributed to the geometric alignment.

The monthly precipitation observational data of the Yangtze River delta are transformed into the temporal evolution of precipitation probability (PP), and its hierarchically distributive characters have been revealed in this paper. Research results show that precipitation of the Yangtze River delta displays the interannual and interdecadal characters and the periods are all significant at a confidence level of more than 0.05. The interdecadal is an important time scale, because it is on the one hand a disturbance of long period changes, and on the other hand it is also the background for interannual change. The interdecadal and 3－7y oscillations have different motion laws in the data-based mechanism self-memory model (DAMSM). Meanwhile, this paper also provides a new train of thought for dynamic modelling. Because this method only involves a certain length of data series, it can be used in many fields, such as meteorology, hydrology, seismology, and economy etc, and thus has a bright perspective in practical applications.

Along the geodesic we calculate the interference phase of the mass neutrinos propagating in the radial direction in the Reissner－Nordstrom field. From the calculation we find that, though there exists electric charge in the gravitational source, the phase increases very little compared with that in the Schwarzschild field.