Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi－Albert (BA) scale-free model with both analytical results and simulations, and find two neighbouring regions, a disassortative one for low degrees and a neutral one for high degrees. The average degree of the neighbours of a randomly picked node is expected to diverge in the limit of infinite network size. As a generalization of the concept of correlation, we also study the correlations of other scalar properties, including age and clustering coefficient. Finally we propose a correlation measurement in bipartite networks.

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.

We give the exact normalized bound state wavefunctions and energy expressions of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.

In this paper, we have extended the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.

In this paper, the definition and criterion of the form invariance of Nielsen equations for relativistic variable mass nonholonomic systems are given. The relation between the form invariance and the Noether symmetry is studied. Finally, we give an example to illustrate the application of the result.

Applying the general projective Riccati equations method, we consider the exact travelling wave solutions for generalized symmetric regularized long-wave equations with high-order nonlinear terms using symbolic computation. From our results, we not only can successfully recover some previously known travelling wave solutions found by using various tanh methods, but also can obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.

An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered.

A noise reduction method based on weighted manifold decomposition is proposed in this paper, which does not need knowledge of the chaotic dynamics and choosing number of eigenvalues. The simulation indicates that the performance of this method can increase the signal-to-noise ratio of noisy chaotic time series.

Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of N-scroll chaotic and hyperchaotic attractors in fourth-order systems. A fourth-order circuit, by introducing additional breakpoints in the modified Chua oscillator, is implemented for the study of generation and synchronization of N-scroll chaotic attractors. This confirms the consistency of theoretical calculation, numerical simulation and circuit experiment. Furthermore, we give a refined and extended study of generating and synchronizing N-scroll hyperchaotic attractors in the fourth-order MCK system and report the new theoretical result, which is verified by computer simulations.

In this paper we study the problem of blind channel identification in chaotic communications. An adaptive algorithm is proposed, which exploits the boundness property of chaotic signals. Compared with the EKF-based approach, the proposed algorithm achieves a great complexity gain but at the expense of a slight accuracy degradation. However, our approach enjoys the important advantage that it does not require the a priori information such as nonlinearity of chaotic dynamics and the variances of measurement noise and the coefficient model noise. In addition, our approach is applicable to the ARMA system.

A study of Hodgkin－Huxley (HH) neuron under external sinusoidal excited stimulus is presented in this paper. As is well known, the stimulus frequency is to be considered as a bifurcate parameter, and numerous phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the stimulus frequency less than 2f_B (f_B being the base frequency in this paper), the simulation results demonstrate that the single HH neuron could completely convey the sinusoidal signal in anti-phase into interspike interval (ISI) sequences. We also report, perhaps for the first time, another kind of phenomenon, the beat phenomenon, which exists in the phase dynamics of the ISI sequences of the HH neuron stimulated by a sinusoidal current. It is shown furthermore that intermittent transition results in the general route to chaos.

A two-pion correlation function at small relative momentum for pion sources with transverse and longitudinal expansions in relativistic heavy ion collisions is obtained using two-pion interferometry at small relative momentum, and the relations between the real and apparent parameters of the pion source are given. The relations can be used to extract both the temperature and the transverse and longitudinal expansion velocities of pion sources and to verify the correctness of relativistic transformation T′=T\sqrt {1-v^2} of temperature in relativistic statistical mechanics and thermodynamics.

By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ_q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity 〈I〉 and variance λ_2 (0) for both below and above the threshold operation, and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ_q makes the 〈I 〉－τ curves exhibit a "re-entrant phase transition". Whether the laser is above or below the threshold, the whole 〈I 〉－τ curve moves down as
λ_q increases; however, when λ_q=1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ_2(0)－p′ curve being suppressed (here p′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ_2 (0)－p′ curve as a function of λ_q is similar to that of the 〈I 〉－τ curve against λ_q: that is, whether the laser is above or below the threshold, the λ_2 (0)－p′ curve moves up as λ_q increases; however, when λ_q=1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.τ

We report the experiments on the optical breakdown and filamentation of femtosecond laser pulses propagating in air at a kHz repetition rate and with several hundreds micro-joule-energy. A 10m-long filament and its breakup and merging at the nonlinear focal region produced by modulational instability of femtosecond laser pulses in air are observed. A simple model based on the nonlinear Schr?dinger equation coupled with multiphoton ionization law is presented to explain the several experimental results.

We report a high-repetition-rate optical parametric generator (OPG) with a periodically poled lithium niobate (PPLN) crystal pumped by an acousto-optically Q-switched CW-diode-end-pumped Nd:YVO_4 laser. For the maximum 1064nm pump power of 970mW, the maximum conversion efficiency is 32.9% under the conditions of 250℃, 1064nm pulse repetition rate of 22.6kHz and pulse width of 12ns, and the PPLN OPG threshold in the collinear case is less than 23.7μJ. The output power increases with the increase of the crystal temperature. The 1485－1553nm signal wave and 3383－3754nm idler wave are obtained by changing the temperature and the angle of the PPLN crystal.

Hartree－Fock and density functional theory (DFT) methods were employed to study poly (vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] molecular chains with different VDF contents. The dependence of dipole moment of P(VDF-TrFE) chains on VDF content obtained from our calculation is in good agreement with the experiment. The TrFE monomer plays an important role in introducing the gauche bond into copolymer chains. A possible mechanism was interpreted.

The effect of the Bloch－Siegert shift on a strongly driven transition is studied in a three-level double-resonance configuration and the result is presented in this paper. We show that when a resonantly driven transition is probed to a third level, the Bloch－Siegert shift leads to an asymmetric Autler－Townes doublet. An important conclusion is that the asymmetry depends only on the driving field intensity, in contrast to a previous study where it is reported that the asymmetry depends not only on the driving field intensity but also on the characteristics of the three-level system. Our result implies an alternative way of measuring the Bloch－Siegert shift.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Measurements of electric field fluctuations, Reynolds stress and poloidal flow have been performed in the boundary region of the HT-7 tokamak using a Langmuir probe array. Sheared radial electric field and poloidal flow have been found in the vicinity of the limiter and the turbulence has been clearly modified in this region. Furthermore, the electrostatic Reynolds stress component shows a radial gradient close to the velocity shear layer location. All results here indicate that the radial gradient of Reynolds stress may play an important role in the driving of poloidal flows in the plasma boundary region.

Energy loss due to a fast-electron beam interacting with the hot plasma at a high density is analysed theoretically. By splitting the particle density fluctuations into the individual part due to the random thermal motion of the individual electrons and the collective part due to plasma－wave excitation, we are concerned with the collective interaction of the relativistic plasma electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the "Debye length" with the modification of the relativistic effect. And finally we calculate the energy loss of a fast-electron beam due to the excitation of collective oscillation in the hot plasma.

Strong drop of Hα emission has been observed on the HL-1M tokamak by means of a detector array while a pellet crosses the q=1 surface. In this article, the q=1 surface has been determined precisely by the interval and the shape of the Hα emission striations on the pellet trajectory due to the variation of pellet ablation rate. The q-profile and current density distribution at the plasma centre region have been calculated according to the pellet ablation rate and the magnetic shear feature.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Shell-model molecular dynamics method is used to study the melting temperatures of MgO at elevated temperatures and high pressures using interaction potentials. Equations of state for MgO simulated by molecular dynamics are in good agreement with available experimental data. The pressure dependence of the melting curve of MgO has been calculated. The surface melting and superheating are considered in the correction of experimental data and the calculated values, respectively. The results of corrections are compared with those of previous work. The corrected melting temperature of MgO is consistent with corrected experimental measurements. The melting temperature of MgO up to 140GPa is calculated.

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

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

Magnetism and magnetic entropy changes in LaFe_{11}Al_2C_x (x=0.0, 0.2 and 0.5) compounds have been investigated. The Curie temperature T_C is conveniently controlled from 200K to room temperature by varying the carbon concentration. Large magnetic entropy change is obtained over a wide temperature range due to the high magnetization and the drastic decrease in the magnetization around T_C. The large magnetic entropy change in wide temperature range, low cost and the convenience of controlling T_C suggest that the LaFe_{11}Al_2C_x compounds are promising candidates for magnetic refrigerants in the corresponding temperature range.

We report on the magnetic properties and magnetocaloric effects of Mn_5Ge_{3-x}Ga_x compounds with x=0.1, 0.2, 0.3, 0.4, 0.6 and 0.9. All samples crystallize in the hexagonal Mn_5Si_3-type structure with space group P6_3/mcm and order ferromagnetically. The Curie temperature of these compounds decreases with increasing x, from 306K (x=0.1) to 274K (x=0.9). The average Mn magnetic moments increases with increasing Ga content, reaching a maximum value at x=0.6. The magnetic entropy changes in these compounds are determined from the temperature and field dependence of the magnetization using the thermodynamic Maxwell relation. The Ga substitution has two kinds of influence on the magnetocaloric effect (MCE) of Mn_5Ge_3. One is that the magnitude of the magnetic entropy change decreases, the other is that the MCE peak becomes broadened.

Er^{3+}- and Er^{3+}/Yb^{3+}-doped lead germanate glasses that are suitable for use in fibre lasers and optical amplifiers as well as optical waveguide devices have been fabricated and characterized. The absorption spectra from near-infrared to visible were obtained and the Judd－Ofelt parameters were determined from the absorption band. Intense and broad 1.53μm infrared fluorescence and visible upconversion luminescence were observed under 976 nm diode laser excitation. For 1.53μm emission band, the full widths at half-maximum are 36, 37, 51 nm for GPE, GPYE and GPFE samples, respectively. For frequency upconversion emission, the intense bands centred at around 524, 545, 657nm are due to the {}^4S_{3/2}+{}^2H_{11/2}→{}^4I_{15/2} and {}^4F_{9/2}→{}^4I_{15/2} transitions of Er^{3+} ions. The quadratic dependence of the green and red emissions on excitation power indicates that the two-photon absorption process occurs under the 976nm excitation.

The retrospective time integration scheme presented on the principle of the self-memory of the atmosphere is applied to the mesoscale grid model MM5, constructing a mesoscale self-memorial model SMM5, and then the short-range prediction experiments of torrential rain are performed in this paper. Results show that in comparison with MM5 the prediction accuracy of SMM5 is obviously improved due to its utilization of multiple time level past observations, and the precipitation area and intensity predicted by SMM5 are closer to observational fields than those by MM5.