In this paper, we study the structural stability of singular discrete systems with perturbations in coefficient matrices. Some sufficient and necessary conditions of structurally stable singular discrete systems are given. Two kinds of structurally stable normal compensators are discussed.

An Ehresmann connection on a constrained state bundle defined by nonlinear differential constraints is constructed for nonlinear nonholonomic systems. A set of differential constraints is integrable if and only if the curvature of the Ehresmann connection vanishes. Based on a geometric interpretation of d－δ commutation relations in constrained dynamics given in this paper, the complete integrability conditions for the differential constraints are proven to be equivalent to the three requirements upon the conditional variation in mechanics: (1) the variations belong to the constrained manifold; (2) the time derivative commutes with variational operator; (3) the variations satisfy the Chetaev's conditions.

In this paper, various waves in the Oregonator model are investigated in detail. The existence of planar waves (in particular, spiral waves) is rigorously proven and their linear stability is analysed. In addition, some non-planar waves in the model are also presented.

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.

The dyadic Green's function for an unbounded gyroelectric chiral medium is formulated in the Fourier domain in cylindrical coordinates. After a triple Fourier integral of the dyadic Green's function has been obtained, the integral is reduced by performing the integration over the transverse Fourier variable.

In this paper we investigate further the method for controlling the uncertain Lü system via adaptive backstepping. The Lü system is transformed into the so-called general strict-feedback form. Then a novel control method is designed for controlling the uncertain Lü system. Especially, this method can overcome the singularity problem. Numerical simulations show the effectiveness and feasibility of this approach.

We present the topology of ^{16}O fragmentation at 60 A GeV in reactions with emulsion nuclei. We discuss the multiplicity distributions of projectile fragments, charged secondaries and their dependence on the target residues.

The two-, four-, five- and fourteen-state approximations of the impact parameter method have been applied to the excitation of hydrogen atoms by proton (p) and antiproton (\overline p) impact. The effect of both channel and back couplings on the 2s and 2p excitations are investigated. The total cross sections are calculated for incident energies ranging from 1 to 2500 keV. It is found that the effect of both channel and back couplings on the antiproton-induced reactions is greater than on that induced by protons. We compare the results with those of other theoretical and experimental works.

Sputtering yield and kinetic energy distribution (KED) of Al particles from an Al_{2}O_{3} sample bombarded with 1－5 MeV Si ions have been simulated using the molecular dynamics method. These have also been measured experimentally with a conventional time-of-flight facility. In the simulation, a new interatomic potential specific to the Al_{2}O_{3} target was developed, and both the nuclear energy loss S_{n} and electronic energy loss S_{e} were taken into consideration. By carefully adjusting the simulation parameters, the simulated sputtering yields fit well with the experimental results, and the simulated KED of Al particles also fits roughly with the experimental KED after being modified theoretically.

We have established the master equation for the micromaser with a Kerr medium. We have studied the photon statistics of the micromaser with a Kerr medium field and analysed the influence of the Kerr effect on the photon statistics. The influence of the Kerr effect on the photon statistics is different in two regimes. In the thermal-atom regime, the Kerr effect produces quantum noise, and decreases the mean photon number. In the ultracold-atom regime, with the increase of the nonlinear parameter of the Kerr medium, the stability of the mean photon number and the normalized variance enhances the mean photon number, and the normalized variance exhibits collapse-revival phenomena periodically, their resonance peaks become lower, and the photon statistics of more and more regions are sub-Poissonian.

We have studied the spectral behaviour of few-cycle soliton pulses in a non-resonant two-level atom medium by solving the full Maxwell－Bloch equations. It is demonstrated further that the carrier effects play an important role in the propagation of the few-cycle pulse laser. When the frequency detuning is not very large, both the population distribution and the refractive index of the medium follow the oscillatory carrier field instantaneously; in this case, carrier-wave compression or carrier shock occurs, and a supercontinuum broader than that in the resonant medium may be generated. When the frequency detuning is large, the carrier shock is weak and the spectrum is not continuous, only showing an odd harmonic radiation.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

We report on our numerical studies of the Axelrod model for social influence in small-world networks. Our simulation results show that the topology of the network has a crucial effect on the evolution of cultures. As the randomness of the network increases, the system undergoes a transition from a highly fragmented phase to a uniform phase. We also find that the power-law distribution at the transition point, reported by Castellano et al, is not a critical phenomenon; it exists not only at the onset of transition but also for almost any control parameters. All these power-law distributions are stable against perturbations. A mean-field theory is developed to explain these phenomena.

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

A variational calculation is presented for the ground-state properties of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles. The relationship between the exciton states and structure parameters of QDQW nanoparticles is investigated, in which both the heavy-hole and the light-hole exciton states are considered. The results show that the confinement energies of the electron and hole states and the exciton binding energies depend sensitively on the well width and core radius of the QDQW structure. A detailed comparison between the heavy-hole and light-hole exciton states is given. Excellent agreement is found between experimental results and our calculated 1s_{e}－1s_{h} transition energies.

In this paper, we establish a one-dimensional random nanocrystalline chain model, we derive a new formula of ac electron－phonon－field conductance for electron tunnelling transfer in one-dimensional nanometre systems. By calculating the ac conductivity, the relationship between the electric field, temperature and conductivity is analysed, and the effect of crystalline grain size and distortion of interfacial atoms on the ac conductance is discussed. A characteristic of negative differential dependence of resistance and temperature in the low-temperature region for a nanometre system is found. The ac conductivity increases linearly with rising frequency of the electric field, and it tends to increase as the crystalline grain size increases and to decrease as the distorted degree of interfacial atoms increases.

Highly c-axis oriented MgB_{2} thin films with T_{c}^{onset} of 39.6K were fabricated by magnesium diffusing into pulsed-laser-deposited boron precursors. The estimation of critical current density J_{c}, using hysteresis loops and the Bean model, has given the value of 10^{7} A/cm^{2} (15 K, 0 T), which is one of the highest values ever reported. The x-ray photoemission study of the MgB_{2} thin films has revealed that the binding energies of Mg 2p and B 1s are at 49.4 eV and 186.9 eV, which are close to those of metallic Mg and transition-metal diborides, respectively.

The dielectric constant of an incipient ferroelectric EuTiO_{3} exhibits a sharp decrease at about 5.5K, at which the antiferromagnetic ordering of the Eu spins simultaneously appears. This fact indicates the existence of a coupling between the magnetism and dielectric properties of EuTiO_{3}. We propose a possible coupling mechanism between the magnetic and electrical subsystems as -g\dsum_{l} \dsum_{〈i,j〉}q^{2}_{l}\vec S_{i}·\vec S_{j}. In the framework of soft-mode theory, we have obtained analytically a dielectric constant expression related to the spin correlation of nearest neighbours of Eu ions.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

The structures of optically-thick accretion discs with radial advection have been investigated by the iteration and integration algorithms. The advective cooling term changes mostly the inner part of disc solution, and even results in an optically-thick advection-dominated accretion flow (ADAF). Three distinct branches－the outer Shakura－Sunyaev disc (SSD), the inner ADAF and the middle transition layer－are found for a super-Eddington disc. The SSD－ADAF transition radius can be estimated as 18(\dot{M}/\dot{M}_{E})R_{G} where R_{G} is the Schwarzschild radius, \dot{M} is the mass accretion rate and \dot{M}_{E} is the Eddington accretion rate. SSD solutions calculated with the iteration and integration methods are identical, while ADAF solutions obtained by these two methods differ greatly. Detailed algorithms and their differences have been analysed. The iteration algorithm is not self-consistent, since it implies that the dimensionless advection factor ξ is invariant, but in the inner ADAF region the variation of ξ is not negligible. The integration algorithm is always effective for the whole region of an optically-thick disc if the accretion rate is no smaller than 10^{-4}\dot{M}_{E}. For optically-thin discs, the validity of these two algorithms is different. We suggest that the integration method be employed to calculate the global solution of a disc model without assuming ξ to be a constant. We also discuss its application to the emergent continuum spectrum in order to explain observational facts.

Nanometre-sized gold particles embedded in BaTiO_{3} composite thin films (Au/BaTiO_{3}) were fabricated by the pulsed laser deposition technique. The films were grown on MgO (100) substrates at 700℃. The crystalline property of the films was studied with x-ray diffraction. X-ray photoelectron spectroscopy was used to check the Au composition and chemical nature for the deposited films. The absorption peak due to the surface plasmon resonance of Au particles was observed at the wavelength of about 570 nm, which increased as the metal particle size was increased. The nonlinear optical properties of the Au/BaTiO_{3} films were determined using the z-scan method at the wavelength of 532 nm, which was close to the resonant frequency. The real and imaginary parts of the third-order nonlinear susceptibility χ^{(3)} at an Au concentration of about 6.7 at.% were determined to be 6.62×10^{-7} esu and -6.24×10^{-8} esu, respectively. The films showed a very large absorption, masking the nonlinear refraction effect at high metal concentrations.

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