The exact bound state wavefunctions and energy equations of Klein－Gordon and Dirac equations are given with equal scalar and vector potential s(r)=v(r)=V(r)/2=V_0tanh^2(r/d). The relation between the energy equation and that of relativistic harmonic is discussed.

The exact normalized bound state wavefunctions and energy equations of Klein－Gordon equation with equal scalar and vector ring-shaped Kratzer-type potential have been obtained.

In a Kerr－Newman－Kasuya field we have obtained expressions of the acceleration effect and also studied the special case (v^i=0). We find that in this field, the acceleration of a falling particle has both radial and transverse components. The acceleration effects of electric charge q and magnetic charge φ are also discussed, separately.

In this paper we consider two coupled scalar fields during the inflation as a dynamical system. With the Poincaré section method, we investigate the evolution of the coupled scalar fields system. We find that the evolution of the system changes from a regular motion into a chaotic motion when the energy density and the coupling constant of the system increase.

A new conserved quantity of non-Noether symmetry for the mechanical systems with differential constraints is studied. First, the differential equations of motion of the systems are established. Then, the determining equations and restriction equations of the non-Noether symmetry are obtained and a new conserved quantity is given. Finally, an example is given to illustrate the application of the results.

Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant (2+1)-dimensional soliton systems like the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) model, the generalized Nizhnik－Novikov－Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations.

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.

By proposing a so-called extended hyperbolic complex (EHC) function method, an Ernst-like (p+2)×(p+2) matrix EHC potential is introduced for the stationary axisymmetric (SAS) Einstein－Maxwell theory with p Abelian gauge fields (EM-p theory, for short), then the field equations of the SAS EM-p theory are written as a so-called Hauser－Ernst-like self-dual relation for the EHC matrix potential. Two Hauser－Ernst-type EHC linear systems are established, based on which some new parametrized symmetry transformations for the SAS EM-p theory are explicitly constructed. These hidden symmetries are found to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac－Moody algebra su(p+1,1)\otimes R(t,t^{-1}) and Virasoro algebra (without centre charges). All of the SAS EM-p theories for p=0,1,2,… are treated in a unified formulation, p=0 and p=1 correspond, respectively, to the vacuum gravity and the Einstein－Maxwell cases.

Using Newtonian forms for equations of motion, we consider the motion of particles and photons in the dilaton spacetime. Some classical gravitational effects, such as the bending of light rays, the perihelion advance of a planet, the delay of radar echo, and the gravitational redshifts, have been investigated. The results show that the gravitational effects arising from the dilaton can be observed provided that the dilaton is large enough.

A simple branch of solution on a bifurcation diagram, which begins at static bifurcation and ends at boundary crisis (or interior crisis in a periodic window), is generally a period-doubling cascade. A domain of solution in parameter space, enclosed by curves of static bifurcation and that of boundary crisis (or the interior of a periodic window), is the trace of branches of solution. A P-n branch of solution refers to the one starting from a period-n (n≥1) solution, and the corresponding domain in parameter space is named the P-n domain of solution. Because of the co-existence of attractors, there may be several branches within one interval on a bifurcation diagram, and different domains of solution may overlap each other in some areas of the parameter space. A complex phenomenon, concerned both with the co-existence of attractors and the crises of chaotic attractors, was observed in the course of constructing domains of steady state solutions of the Hénon map in parameter space by numerical methods. A narrow domain of period-m solutions firstly co-exists with (lies on) a big period-n (m≥3n) domain. Then it enters the chaotic area of the big domain and becomes period-m windows. The co-existence of attractors disappears and is called the landing phenomenon. There is an interaction between the two domains in the course of landing: the chaotic area in the big domain is enlarged, and there is a crisis step near the landing area.

An S-box modified one-way coupled map lattice is applied as a chaotic cryptograph. The security of the system is evaluated from various attacks currently used, including those based on error function analysis, statistical property analysis, and known-plaintext and chosen-ciphertext analytical computations. It is found that none of the above attacks can be better than the brute force attack of which the cost is exhaustively quantitated by the key number in the key space. Also, the system has fairly fast encryption (decryption) speed, and has extremely long period for finite-precision computer realization of chaos. It is thus argued that this chaotic cryptosystem can be a hopeful candidate for realistic service of secure communications.

Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension. Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.

By using the Fourier transform method, analytical expressions for the axial power spectrum and near-field intensity in the spacetime domain of chirped Gaussian pulses diffracted at an aperture are derived, which permit us to study changes in spectral and temporal profiles of the chirped Gaussian pulses both analytically and numerically. Detailed numerical results and physical analysis show that spectral anomalies take place in the neighbourhood of certain critical distances, and the shifting of maximum and splitting of temporal intensity profiles appear. In particular, for ultrashort chirped pulses, there exists also spectral switch. Besides the truncation parameter, the chirp parameter and pulse duration affect the behaviour of spectral switches.

The magnetism and magnetoresistance (MR) in a series of oxygen-deficient La_{2/3}Ca_{1/3}MnO_{3-δ} (LCMO) thin films have been investigated. Compared with the films with stoichiometric oxygen concentration, the oxygen-deficient LCMO thin films show a spin-glass-like behaviour at low temperatures, and a positive MR effect above the metal－insulator transition temperature. The mechanism of such unusual phenomena is discussed.

A sample of 1233 events is used to study the general characteristics of {}^{16}O－Em interactions at 4.5 A GeV/c. Multiplicity and angular distributions of slow particles and correlations among them are discussed. The present data are compared with the corresponding results from the interactions of other projectiles at the same energy and also the same projectile at different energies. The results indicate that black particle production is independent of the energy and mass of the projectile, but for grey particles it is dependent on the mass of projectile.

Lie algebraic methods are used in the analysis of the nonlinear transport of charged particle beams in solenoid lenses. Space charge effects are included. The particle distribution we used is a K－V type. Similar procedures can also be used for magnetic dipoles, quadrupoles, sextupoles and other optic elements.

The properties of electromagnetic waves propagating inside isotropic or uniaxial dielectric media moving in an arbitrary direction are analysed. The scalar products of electromagnetic field vectors inside these moving media are investigated in the kEB system from Maxwell's equations and Lorentz-covariant constitutive relations. Several important equations are derived. They are useful in discussing problems such as the energy density and radiation pressure, which are of interest in theoretical studies and many application subjects.

We propose a special two-photon state which is completely transparent in a 50/50 beam splitter. This effect is caused by the destructive two-photon interference and shows the signature of photon entanglement. We find that the symmetry of the two-photon spectrum plays the key role for the properties of two-photon interference.

We investigate the amplification mechanism in a four-level system by both the density-matrix and quantum-jump approaches. We show that the asymmetry between three-photon stimulated emission and one-photon absorption process is responsible for the inversionless amplification of the probe field. We also investigate the effects of spontaneously generated coherence (SGC) on the probe gain, and find that due to the SGC, the probe gain can be greatly enhanced and can be modulated by changing the relative phase between the applied fields.

In this paper, frequency-doubled Nd:YAG laser's phase conjugation has been investigated experimentally using resonant degenerate four-wave mixing (DFWM). The iodine solution was used as resonant medium. In this way, the energy of the DFWM phase conjugation beam arrived at 43μJ/pulse while the total pump beam's energy reached 8mJ/pulse. The relation between the pulse energy of the DFWM phase conjugation beam and that of the pump beam was investigated. We also measured the optical field distributions of pump beam and DFWM phase conjugation beam, from which it can be noticed that the DFWM phase conjugation can improve the laser beam quality. At the same time, we observed the influence of the pump beam's disturbance on the DFWM signal.

The coupling effect and stability property of symmetric bright holographic soliton pairs have been investigated numerically. Results show that when any one of the two solitary beams from a pair is perturbed in amplitude or width, both beams will be affected by such a perturbation via the coupling effect between the beams, thus resulting in both beams propagating in the medium without a constant shape; however, these two solitary beams are still stable against small perturbations. When both solitary beams from a pair are perturbed simultaneously in amplitude, for some given absolute values of the perturbations, the two beams are stable against these perturbations if both beams are perturbed with the same sign, whereas are unstable with the different signs. When the two beams are simultaneously perturbed in width, both beams exhibit their stability property similar to that when only one beam is perturbed no matter whether both perturbations have the same or different signs.

A principle of selecting relaxation parameter was proposed to observe the limit computational capability of the incompressible LBGK models developed by Guo ZL (Guo model) and He SY (He model) for high Reynolds number flow. To the two-dimensional driven cavity flow problem, the highest Reynolds numbers covered by Guo and He models are in the range 58000－52900 and 28000－29000, respectively, at 0.3 Mach number and 1/256 lattice space. The simulation results also show that the Guo model has stronger robustness due to its higher accuracy.

A new variation method is extended to study the atomic systems with higher nuclear charges and in more highly excited states. The non-relativistic energies of 1s^2np (n≤9) states for the lithium-like systems from Z=11 to 20 are calculated using a full-core-plus-correlation method with multi-configuration interaction wavefunctions. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation corrections. The fine structures are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli－Breit approximation. The quantum-electrodynamics correction is also included. Our results are compared with experimental data in the literature.

Electron-induced Hf-, W-L-shell partial, total production cross sections, mean ionization cross sections and Hf-L_3-shell ionization cross sections (at two energies) have been measured as functions of electron energies (from near threshold to 36keV). The influence of electrons reflected from the backing of the thin targets on measured results was corrected using a model to relate to the electron transport process. The mean paths of electron multi-scattered in the target itself (including forward and backward scattering) were calculated by means of Monte Carlo program (EGS4) and they were used to correct measured results. A comparison with both theoretical predictions was given.

The equilibrium geometries and the atomization energies of Cu_n(n≤9) clusters have been calculated using the B3LYP/LANL2DZ method. It is shown that the clusters do not copy the bulk structures and undergo significant geometrical changes with size and the atomization energy per atom increases monotonically with size. By analysing the energy level distribution, the Fermi level, HOMO－LUMO gaps, the electron affinities and the ionization potentials are calculated and the results are in reasonable agreement with experiment. These electronic properties are found to be strongly structure dependent, which can be used to determine which of the low-lying structures is observed experimentally.

CROSS DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

We have studied the kinetic behaviours of irreversible aggregation－annihilation models with cluster removals. In the models, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible annihilation reaction occurs simultaneously between two different species; meanwhile, the clusters of large size are gradually removed from the system. In a mean-field limit, we obtain the general solutions of the cluster-mass distributions for the cases with an arbitrary removal probability. We found that the cluster-mass distribution of either species satisfies a generalized or modified scaling form. The results also indicate that the evolution behaviours of the systems depend strongly on the details of the reaction events.

We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate K(i;j)=K′(i;j)∝i^uj^v at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with u+v≤3 and u<2 approaches a conventional scaling form, which reduces to the Smoluchovski form in the u=1 case. On the other hand, for the system with u<2, the average aggregate size S(t) grows exponentially in the u+v=3 case and as (tlnt)^{1/(5-2u)} in another special case of v=u-2. Moreover, this typical size S(t) grows as t^{1/(3-u-v)} in the general u-2

Using Langevin simulations, we have investigated numerically the depinning dynamics of driven two-dimensional colloids subject to the randomly distributed point-like pinning centres. With increasing strength of pinning, we find a crossover from elastic to plastic depinnings, accompanied by an order to disorder transition of state and a substantial increase in the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity－force dependence (VFD) and the transverse motion is almost none. In addition, the scaling relationship between velocity and force is found to be valid above depinning. However, when one enters the plastic regime, a peak appears in the differential curves of VFD and transverse diffusion occurs above depinning. Furthermore, history dependence is found in the plastic regime.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The wide-gap semiconductor TiO_2 nanoparticles with and without dye sensitization have been studied by small angle x-ray scattering using synchrotron radiation. Surface properties of the colloidal TiO_2 nanoparticles have been analysed in terms of the surface fractal dimensions (D_s), showing that D_s changes from 3.25 to 2.34 when TiO_2 nanoparticles are sensitized by ATRA (all-trans-retinoic acid), which reveals that the surface of the particles become relatively smooth after dye sensitization. The size distribution of gyration radius of TiO_2 nanoparticles in the colloids M(R_g) has been successfully determined by the Shull－Roess method. The main peak of M(R_g) for the unsensitized TiO_2 colloid is located at 2.1nm, corresponding to a spherical diameter of 5.4nm, and this value for the ATRA sensitized TiO_2 increases to 2.4nm, indicating a spherical diameter of 6.4nm. Such a size enlargement of TiO_2 nanoparticles suggests that there is a coating of ATRA on the TiO_2 surface, supporting the view that a monolayer of the dye has been attached to the surface of the TiO_2 nanoparticle.

The deposition of a single Si adatom on the p(2×2) reconstructed Si(100) surface has been simulated by an empirical tight-binding method. Using the perfect and defective Si surfaces as the deposition substrates, the deposition energies are mapped out around the research areas. From the calculated energy plots, the binding sites and several possible diffusion paths are achieved. The introduced defects will make the deposition behaviour different from that on the perfect surface.

Beijing Synchrotron Radiation Facility is a partly dedicated synchrotron radiation source operated in either parasitic or dedicated mode. The 3B1A beamline, extracted from a bending magnet, was originally designed as a soft x-ray beamline for submicro x-ray lithography with critical lateral size just below 1μm in 1988 and no change has been made since it was built. But later the required resolution of x-ray lithography has changed from sub-micrometre to the nanometre in the critical lateral size. This beamline can longer more meet the requirement for x-ray nano lithography and has to be modified to fit the purpose. To upgrade the design of the 3B1A beamline for x-ray nano lithography, a mirror is used to reflect and scan the x-ray beam for the nano lithography station, but the mirror's grazing angle is changed to 27.9mrad in the vertical direction, and the convex curve needs to be modified to fit the change; the tiny change of mirror scanning angle is firstly considered to improve the uniformity of the x-ray spot on the wafer by controlling the convex curve.

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

This article presents numerical solutions of the periodic time-dependent Ginzburg－Landau model for the type-II superconductors by a finite-difference approximation. Both the static and dynamical properties of a single vortex are studied as the external magnetic field varies. Vortex and anti-vortex can coexist and annihilate with time in the case of no external magnetic field, while the vortex will approach a steady state in the presence of magnetic field. We also study vortex dynamical behaviours while pinning centres exist in the sample and find that the pinning site, which has a significant potential to keep the vortex from moving, may trap the vortex.

The static and dynamic magnetic properties of a Prussian blue analogue, molecular magnet Cu^Ⅱ_{3}[Fe^Ⅲ(CN)_6]_2·3NH_3·6H_2O were investigated in detail. The H dependence of the linear AC susceptibility, the irreversibility in the field-cooled (FC)/zero-field-cooled (ZFC) magnetization (M_{FC}/M_{ZFC}) and the relaxation of M_{ZFC} suggest that the magnetic system can be visualized as containing a ferromagnetic cluster of spin below T_C, mixed with small spin-glass clusters formed below temperature T_g less than T_C. The observed magnetic properties are explained with a ferromagnetic-spin-glass phase model. The magnetic ordering of the sample occurs below 19.8K.

We deposited high quality ZnO film by electrophoretic deposition (EPD) using high quality ZnO powder prepared by solid-state pyrolytic reaction. X-ray photoelectron spectroscopy (XPS) and the infrared (IR) absorption spectrum clearly indicate that the ZnO phase powder has been prepared. Transmission electron microscope (TEM) imaging and x-ray diffraction (XRD) show that the average grain size of the powder is about 20nm. XRD and selected-area electron diffraction (SAED) reveal that the ZnO film has a polycrystalline hexagonal wurtzite structure. Only a strong ultraviolet emission peak at 390nm can be observed at room temperature.

With laser-cooled cold {}^{87}Rb atoms as a magneto-optical medium, a weak right circularly polarized probe field and frequency modulation technique are used to detect the magnetic distribution of the quadrupole field. A two-peak dispersion-like signal other than that of the usual nonlinear magneto-optical effect mentioned in other papers is obtained.

A simple method for calculating the free-exciton binding energies in the fractional-dimensional-space model for single-quantum-well structure has been extended to quantum-well wires and quantum dots, in which the real anisotropic system is modelled through an effective isotropic environment with a fractional dimension. In this scheme, the fractional-dimensional parameter is chosen via an analytical procedure and involves no ansatz. We calculated the ground-state binding energies of excitons and donors in quantum-well wires with rectangular cross sections. Our results are found to be in good agreement with previous variational calculations and available experimental measurements. We also discussed the ground-state exciton binding energy changing with different shapes of quantum-well wires.