Table of contents

This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result.

In this paper, the Lie-form invariance of the Lagrange system is studied. The definition and the criterion of the Lie-form invariance of the Lagrange system are given. The Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. Finally, two examples are presented to illustrate the application of the results.

Exact travelling wave solutions to some nonlinear equations of fifth order derivatives are derived by using some accurate ansatz methods.

In this paper, the three-dimensional radial position-dependent mass Schrödinger equation is exactly solved through mapping this wave equation into the constant mass Schrödinger equation with Coulomb potential by means of point canonical transformation. The wavefunctions here can be given in terms of confluent hypergeometric functions.

In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein–Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

The divergences at all levels for the statistical entropy of a plane symmetry black hole arising from the massless Dirac field are considered using the brick-wall model. It is shown that if we ignore the usual contribution from the vacuum surrounding the system, then the statistical entropy consists of two parts: one is the linearly divergent term which has the geometric character, the other consists of two logarithmically divergent terms which are not proportional to the surface area of the horizon. The entropy of the Dirac field on extremal plane symmetry spacetime background has higher divergence than usual.

From modern control theory, an active control method to synchronize two modified Chua circuits with each other, which exhibit chaos, is presented. Some sufficient conditions of linear stability of the chaotic synchronization are obtained from rigorous mathematic justification. On the basis of the state-observer, the controller is analytically deduced using the active control. It is shown that this technique can be applied to achieve synchronization of the two systems with each other, whether they are identical or not. Finally, numerical simulations show the effectiveness of the proposed control scheme.

Based on the coupled map lattice models, the mutual relation of spatiotemporally chaotic signals is studied using the symbolic analysis method. Numerical computation results show that the conditional entropy of two directly coupled lattices or that of two indirectly coupled but near lattices has a sharp minimum, whereas the conditional entropy of two distant lattices has no sharp minimum. Thus, the mutual relation of spatiotemporally chaotic signals produced by the coupled map lattice systems can be manifested by the symbolic analysis method.

Fifteen new absorption lines were observed when studying CO₂ absorption spectroscopy by wavelength modulation technique with a distributed feedback laser. The overtone spectra of CO₂ around 1.31μm and the corresponding spectral parameters (i.e. positions, intensities, self-broadening coefficients) are presented. The intensity of the weakest line detected is 2.25163×10⁻²⁷cm⁻¹/(molecule.cm⁻²) at the pressure of 667Pa, with a corresponding absorption of 3.88×10⁻⁸.

The excited states of the ⁷²Ge nucleus were investigated in radioactive decay of ⁷²As. Three new transitions with 1996.58, 2125.59 and 2255.49keV have been found for the first time. One γ-ray with 912.09keV has been placed in the decay scheme for the first time and the placement of 1938.88, 2116.79, 2785.59, 2833.03, 2950.69 and 3338.00keV γ-rays are confirmed again in the present work. One new level at 2027.72keV excitation energy is proposed. The level scheme was established and for a number of levels spin-parity assignments are suggested on the basis of logft values and γ-branching ratios.

Recently multipacting (MP) recalculation of the TeV Energy Superconducting Linear Accelerator (TESLA) resonator was performed. In addition to the normal MP which occurs at a peak electric field of around 40MV/m for the TESLA cavity, another type of multipacting with resonant electron trajectory that is far from the equator is also seen. It occurs at a gradient around 60MV/m to 70MV/m. This result seems to explain some experimental observations.

We investigate the neutronic performance of coupled moderators to be implemented in spallation neutron sources by Monte-Carlo simulation and give the slow neutron spectra for the cold and thermal moderators. CH₄ moderator can provide slow neutrons with highly desirable characteristics and will be used in low-power spallation neutron sources. The slow neutron intensity extracted from different angles has been calculated. The capability of moderation of liquid H₂ is lower than H₂O and liquid CH₄ due to lower atomic number density of hydrogen but we can compensate for this disadvantage by using a premoderator. The H₂O premoderator of 2cm thickness can reduce the heat deposition in the cold moderator by about 33% without spoiling the neutron pulse.

By using the energies of the 1s²nd (n=3–5) and 1s²nf (n=4–6) states for a lithium atom, calculated with the full core plus correlation method, quantum defect functions are obtained which vary smoothly with energy based on quantum defect theory. Then these functions are separately used to construct a system equation to calculate the energies and quantum defects of the 1s²nd and 1s²nf (n=7–11) states for the lithium atom. Separations between the centres of gravity of the nd and nf levels (n=7–11) are also predicted and compared with the experimental and theoretical data available in the literature.

Isotope shifts and hyperfine spectrum of singly ionized neodymium ion was measured by collinear fast-ion-beam laser spectroscopy. The hyperfineA constants and B constants are obtained for the (23230)^o_9/2 level and 4f⁴5d ⁶K_9/2 level, respectively. The optical isotope shifts between seven isotopes in the 580.56 nm of ^{142−145,146,148,150}Nd⁺ line are determined. The configuration admixtures for (23230)^o_9/2 level were quantitatively analysed to be 4f⁴6p, 4f³5d² and 4f³5d6p with mixing coefficients of 67%, 5% and 28%, respectively.

When both intermolecular dipolar couplings (D couplings) and intramolecular scalar couplings (J couplings) exist in a highly polarized multiple-spin liquid, some forbidden nuclear magnetic resonance signals originating from intermolecular multiple-quantum coherences may become observable. Moreover, their multiplet patterns are quite different from what are observed in a multiple-spin system with J couplings only. In this paper, these forbidden resonance peaks and unique multiplet patterns are studied theoretically and experimentally. For comparison and verification, an I₂S₃+X spin system is chosen as an example to present five types of signal patterns from the interactions ofD and J couplings with either selective or non-selective radio-frequency pulse sequences for double-quantum coherences. The multiplet pattern rules for a more general I_pS_q+X_k (p,q,k = 1,2,3,...) spin system are derived as well. It is demonstrated that some unusual multiplet amplitude patterns such as (1:0:–1) may ``magnify'' J splittings, allowing more accurate measurement of J coupling in the case of small J coupling constants and/or in inhomogeneous fields. It is shown that the theoretical predictions, computer simulations and experimental observations are all in agreement with one another very well.

The optical–optical double-resonant multiphoton ionization (OODR-MPI) technique has been applied to the study of the Rydberg states of nitrogen dioxide. The results show that, although the OODR-MPI spectra of NO₂ are composed of regular progression bands at different pump laser intensities, their ionization pathways are different. The NO₂ molecule is ionized through the (3+1+1) double-resonant process as the pump laser intensity is in a high value, or else it is through the (1+2+1) process. The final resonant states in the two ionizing processes have been attributed to different Rydberg states.

The first-principles, all-electron, ab initio calculations have been performed for an the amazing stable planar structure of Ga₅N₅ cluster based on the density functional theory. Electronic structure, electron affinity, ionization potential and binding energy are obtained. No spin magnetic moment is found. The results show that the planar structure of the Ga₅N₅ cluster is stable. It is found that for the planar structure of Ga₅N₅ cluster, three nitrogen atoms in the N₃ subunit bind together with large electron transfer although no free N₃ can exist. This may be important to the stability of the planar structure of the Ga₅N₅ cluster which has the lowest ground-state energy.

A scheme is proposed for the generation of W entangled states for several atoms trapped in a cavity by detecting photon decay. The scheme works in the regime, where the cavity decay rate is larger than the atom-cavity coupling strength. Thus, the requirement for the quality factor of the cavity is greatly loosened, which is of importance in view of experiment. Another advantage of this scheme is that the atoms are always populated in two ground states coupled by Raman transitions, thus the spontaneous emission can also be suppressed.

In this paper, we use the field entropy as a measurement of the degree of entanglement between the light field and the atoms of the system which is composed of two dipole–dipole interacting two-level atoms initially in an entangled state interacting with the single mode coherent field in a Kerr medium. The influence of the coupling constant of dipole–dipole interaction between atoms and the coupling strength of the Kerr medium with the light field and the intensity of the light field on the field entropy are discussed by numerical calculations. It is shown that when the coupling strength of the Kerr medium with the light field is large enough and the light field is strong, the degree of entanglement between the atoms with the light field becomes weaker. The degree of entanglement only changes slightly with the change of the coupling constant of dipole–dipole interaction between atoms.

A quantum identification scheme including registration and identification phases is proposed. The users' passwords are transmitted by qubit string and recorded as a set of quantum operators. The security of the proposed scheme is guaranteed by the no-cloning theorem. Based on photon polarization modulation, an experimental approach is also designed to implement our proposed scheme.

The contribution of multiphoton absorption to open-aperture Z-scan measurements is analysed by coordinate transformation. The approximate closed-form solution is obtained, which is suitable for application in higher-optical power regime. As an example, the coupling between linear absorption and two-photon absorption is discussed in detail.

Ultrafast third-order nonlinear optical responses of GeS₂–Ga₂S₃–CdS glasses have been measured by using femtosecond time-resolved optical Kerr effect (OKE) technique at the wavelengths of 820nm and 640nm respectively. The experimental results show that GeS₂–Ga₂S₃–CdS glasses have large femtosecond third-order optical nonlinear responses and their OKE signals vary considerably with the composition. The relationship of structure-property is discussed by means of Raman spectroscopy analysis, suggesting that the tetrahedron unit [GeS₄] or [GaS₄] plays an important role in the ultrafast third-order nonlinear optical response. In addition, the experimental results also reveal that the ultrafast third-order optical nonlinearity of these glasses does not obey the Miller rule.

H13 die steel was implanted with tungsten using a metal vapour vacuum arc (MEVVA) ion source. When the pulsed beam current density of tungsten ions increased to 6mA.cm⁻², some voids appeared in the high voltage electron microscope (HVEM) micrograph, which would disappear at an annealing temperature of 600 degrees C. HVEM and x-ray diffraction were used for observing the phase structure of the annealed and un-annealed H13 steel after the steel was implanted. Results of wear and hardness tests indicated that whether the voids appear significantly influences the hardness and wear of H13 steel. Reasons for the formation of voids and the relation between the surface mechanical property and voids are discussed in terms of collision theory.

In this paper, the finite current element (FCE) method used in HL-2A is described. The calculation and test results show that the error of the reconstructed boundary given by the FCE method (<3mm) is smaller than that obtained by the current filament method used before (<6mm). Even if some current elements are located out of the plasma boundary, the FCE method can also identify the plasma boundary successfully. If the location of the finite current elements is changed in a certain area, the error of the reconstructed boundary is always very small. By employing a conventional PC (Pentium 4 2.4GHz), the calculation time of one set of plasma discharge parameters does not exceed 1ms. Thus, the FCE method can identify the diverted plasma configuration quickly and accurately. This is essential and important for real-time shape control in HL-2A.

The effect of implanting nitrogen into buried oxide on the top gate oxide hardness against total irradiation does has been investigated with three nitrogen implantation doses (8×10¹⁵, 2×10¹⁶ and 1×10¹⁷cm⁻²) for partially depleted SOI PMOSFET. The experimental results reveal the trend of negative shift of the threshold voltages of the studied transistors with the increase of nitrogen implantation dose before irradiation. After the irradiation with a total dose of 5×10⁵rad(Si) under a positive gate voltage of 2V, the threshold voltage shift of the transistors corresponding to the nitrogen implantation dose 8×10¹⁵cm⁻² is smaller than that of the transistors without implantation. However, when the implantation dose reaches 2×10¹⁶ and 1×10¹⁷cm⁻², for the majority of the tested transistors, their top gate oxide was badly damaged due to irradiation. In addition, the radiation also causes damage to the body-drain junctions of the transistors with the gate oxide damaged. All the results can be interpreted by tracing back to the nitrogen implantation damage to the crystal lattices in the top silicon.

We study the propagation and collision of the compacton-like kinks in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compacton-like kinks is related to the nonlinear coupling parameter C_nl and the potential barrier height V₀ of the double well potential. The velocity of the propagation of the compacton-like kinks is determined by the linear coupling parameter C_l, the nonlinear coupling parameter C_nl and the localization parameter q. Numerical experiments demonstrate that appropriate C_l is not detrimental to a stable propagation of the compacton-like kinks. However, the collision of compacton-like kinks and anti-kinks in the lattice with comparatively smallC_l leads to the emergence of a discrete stationary breather and small amplitude nonlinear oscillation background, while moderate C_l results in the emergence of two deformed kinks with radiating oscillations and lower propagation velocities.

In this paper, we investigate the performance of the well-known optimal velocity car-following model (the OVM) with numerical simulation in describing the acceleration process that is induced by the motion of a leading car with a pre-specified speed profile. Results show that this model is to some extent deficient in performing this process. Modification of the OVM to overcome the deficiency is demonstrated. The linear stability for the modified model is analysed. If the linear stability condition can not be satisfied, phase transitions occur on varying the initial homogeneous headway of the traffic flow.

A novel SiC Schottky barrier source/drain NMOSFET (SiC SBSD-NMOSFET) with field-induced source/drain (FISD) extension is proposed and demonstrated by numerical simulation for the first time. In the new device the FISD extension is induced by a metal field-plate lying on top of the passivation oxide and the width of Schottky barrier is controlled by the metal field-plate. The new structure not only eliminates the effect of the sidewalls but also significantly improves the on-state current. Moreover, the performance of the present device exhibits very weak dependence on the widths of sidewalls.

Various morphology ZnO submicrorods and microrods have been fabricated onto glass substrates through chemical solution growth by the source of zinc acetate (Zn(CH₃COO)₂.2H₂O) and hexamethylene tetraamine ((CH₂)₆N₄). We discuss the influence of PH and the concentration of the solution on the shapes of the as-synthesized ZnO samples. And analyse the growth mechanism. The regular hexagonal ZnO rods align has been made by control of a certain concentration and proper PH. The hexagonal ZnO columns mainly grew in the [002] direction. X-ray diffraction (XRD), scanning electron microscopy (SEM) and photoluminescence (PL) are used to characterize the structure, the morphology and optical property of the samples. The photoluminescence spectrum of hexagonal ZnO columns shows that there are a broad strong red band (650nm) and a broad band in short wavelength which are two overlapped emission bands with the peaks at about 380nm and 430nm.The UV emission (~387nm) comes from recombination of free excitons. The blue emission with peak at 430nm is assigned for the recombination from an electron at interstitial Zn to a hole in VB. The red emission at 650nm is ascribed to the recombination from an electron at Vo²⁺ to a hole in VB.

An analytical expression for the stationary probability distribution of the DC superconducting quantum interference device (SQUID) with a resistively shunted inductance driven by thermal noise is derived from the two-dimensional Fokker–Planck equation. The effects on the SQUID characteristics subject to a large thermal fluctuation with a noise parameter Γ>0.20 are discussed by taking into account the thermal noise in the accuracy of numerical simulation. This theory is valid for a reduced inductance β⩽1. The analytical formulae for the SQUID characteristics, e.g. the circulating current, the average voltage and the voltage modulation, are obtained and discussed. The theory shows that the voltage modulation increases with the shunted inductance more efficiently for a large inductance parameter β and small fluctuation parameter Γ.

High-dose ion implantation of phosphorus into 4H–SiC (0001) has been investigated with three different ion fluxes ranging from 1.0 to 4.0×10¹² P⁺cm⁻².s⁻¹and keeping the implantation dose constant at 2.0×10¹⁵ P⁺cm⁻². The implantations are performed at room temperature and subsequently annealed at 1500 degrees C. Photoluminescence and Raman scattering are employed to investigate the implantation-induced damages and the residual defects after annealing. The electrical properties of the implanted layer are evaluated by Hall effect measurements on the sample with a van der Pauw configuration. Based on these results, it is revealed that the damages and defects in implanted layers can be greatly reduced by decreasing the ion flux. Considering room temperature implantation and a relatively low annealing temperature of 1500 degrees C, a reasonably low sheet resistance of 106Ω/□ is obtained at ion flux of 1.0×10¹² P⁺cm⁻².s⁻¹with a donor concentration of 4.4×10¹⁹cm⁻³.

We investigate the effects of strain and film thickness on the coercivity of La_0.67Ca_0.33MnO₃ films grown on SrTiO₃ and LaAlO₃ substrates. Textured microstructure with the grain [001] pseudo-cubic axis normal to the film surface is obtained. The average grain size decreases with decreasing film thickness t. The magnetic anisotropy depends upon the substrate-induced strain. Firstly, the intrinsic coercivity _iH_C increases as t varies from 5 nm to 10 nm, then attains a maximum at t~ 10–25nm. A further increase in t yields a gradual reduction of_iH_C. By the analysis of the dependence of _iH_C on the measured direction of magnetic field, the coercivity mechanism is assumed to be mainly determined by the nucleation of reversed domain and the domain wall pining for t⩽10nm and t⩾25nm, respectively, which were further verified by the investigation of the initial magnetization curves for the LCMO/STO films with t=5, 10, 25 and 400nm and the minor magnetic loops for the LCMO/LAO films with t=5 and 50nm. Moreover, the size of the inhomogeneous region in which the nucleation or pinning takes place is discussed.

SrTiO₃ thin films were deposited on vitreous silica substrates by metalorganic decomposition (MOD). The films are polycrystalline cubic in structure with the lattice constants ofa=0.39nm. Their optical constants (refractive index n and extinction coefficientk) were calculated by the envelope method from the transmittance spectra in the wavelength range of 190nm to 1100nm. The refractive index of the present films is found to be higher than that of the other SrTiO₃ films prepared by RF sputtering, sol–gel and chemical vapour deposition. The dispersion of the refractive index in the films follows the single electronic oscillator model with oscillator strength (S₀) of 0.88×10¹⁴m⁻² and oscillator energy (E₀) of 6.40eV. The optical band gap of the films was estimated to be 3.68eV.

Er-doped SiO_x films were synthesized at 500 degrees C by ion beam assisted deposition technique and annealed at 800 and 1100 degrees C for 2h in the air atmosphere. The analysis by using energy dispersive x-ray spectroscopy showed that the ratio of Si to O decreased from 3 in the as-deposited films to about 1 in the annealed films. The investigation by using transmission electron microscopy and x-ray diffraction indicated that annealing induces a microstructure change from amorphous to crystalline. The grain sizes in the films were about 10 and 40nm when annealed at 800 and 1100 degrees C, respectively. The films annealed at temperatures of 800 and 1100 degrees C exhibited a sharp photoluminescence (PL) at 1.533μm from the Er centres when pumped by 980nm laser. The influence of microstructure and grain size on the PL from Er-doped SiO_x films has been studied and discussed.

Sedimentation of particles in inclined and vertical vessels is numerically simulated using a finite volume method where the Eulerian multiphase model is applied. The particulate phase as well as the fluid phase is regarded as a continuum while the viscosity and solid stress of the particulate phase are modelled by the kinetic theory of granular flows. The numerical results show an interesting phenomenon of the emergence of two circulation vortices of the sedimentation flow in a vertical vessel but only one in the inclined vessel. Several sensitivity tests are simulated to understand the factors that influence the dual-vortex flow structure in vertical sedimentation. Results show that a larger fluid viscosity makes the two vortex centres much closer to each other and the boundary layer effect at lateral walls is the key factor to induce this phenomenon. In the fluid boundary layer particles settle down more rapidly and drag the local carrier fluid to flow downward near the lateral walls and thus form the dual-vortex flow pattern.

At present, most of the statistical prediction models are built on the basis of the hypothesis that the time series or the observation data are linear and stationary. However, the observations are ordinarily nonlinear and non-stationary in nature, which are very difficult to be predicted by those models. Aiming at the nonlinearity/non-stationarity of the observation data, we introduce a new prediction scheme in this paper, in which firstly using the empirical mode decomposition the observations are stationarized and a variety of intrinsic mode functions (IMF) are obtained; secondly the IMFs are predicted by the mean generating function model separately; finally the predictions are used as new samples to fit and predict the original series. Research results show that the individual IMF, especially the eigen-IMF (namely eigen-hierarchy), has more stable predictability than the traditional methods. The scheme may effectively provide a new approach for the climate prediction.

The overtone spectra of H₂SiCl₂ molecule in the regions of 2000–9000cm⁻¹and 12000–12900cm⁻¹at room temperatures have been studied by use of high-resolution Fourier transform spectroscopy and sensitive-intracavity-laser absorption spectroscopy, respectively. The variations of vibrational quantum numbers Δ V_SiH=1, 2, 3, 4 and 6 for the overtones of the SiH stretching have been analysed and assigned with the local mode model and the normal mode model. The values of harmonic frequency ω_m, anharmonicity constant χ_m, bond coupling constant λ, the Morse oscillator parameters D_e, α and interaction force constant f_rr'are derived from the experimental spectrum with nonlinear least-squares fitting. The most striking feature of the SiH₂Cl₂ is that the larger the vibrational energy, the smaller the energy difference between a couple of lowest stretching states of a given manifold and finally, the couple of lowest stretching states are degenerated within the experimental error for Δ V_SiH⩾4 vibrational manifolds. The degenerate energy level structure resembles that of a diatomic Morse oscillator; the transition energies show a remarkable fit to the Birge–Sponer relation. The high vibrational states can be described straightforward with a SiH diatomic Morse oscillator wavefunction, this is an indication of vibrational bond localization.