Chin. Phys. B
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CN 11-5639/O4
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Chin. Phys. B  
  Chin. Phys. B--2002, Vol.11, No.12
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Structural stability in discrete singular systems

Wu Jian-Rong, Yang Cheng-Wu
Chin. Phys., 2002, 11 (12): 1221-1227 doi: 10.1088/1009-1963/11/12/001
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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.

A connection theory for a nonlinear differential constrained system

Xu Zhi-Xin, Guo Yong-Xin, Wu Wei
Chin. Phys., 2002, 11 (12): 1228-1233 doi: 10.1088/1009-1963/11/12/002
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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.

Existence and linear stability of planar waves in the Oregonator model

Zhou Tian-Shou, He Xiao-Lan
Chin. Phys., 2002, 11 (12): 1234-1239 doi: 10.1088/1009-1963/11/12/003
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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.

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model

Shen Jian-Qi, Zhu Hong-Yi, Fu Jian
Chin. Phys., 2002, 11 (12): 1240-1244 doi: 10.1088/1009-1963/11/12/004
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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.

Dyadic Green's function for an unbounded gyroelectric chiral medium in cylindrical coordinates

Li Kai, Pan Wei-Yan
Chin. Phys., 2002, 11 (12): 1245-1248 doi: 10.1088/1009-1963/11/12/005
Full Text: [PDF 218 KB] (Downloads:330)
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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.

Adaptive backstepping control of the uncertain Lü system

Yu Yong-Guang, Zhang Suo-Chun
Chin. Phys., 2002, 11 (12): 1249-1253 doi: 10.1088/1009-1963/11/12/006
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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.

Large third-order optical nonlinearity in Au nanometre particle doped BaTiO3 composite films near the resonant frequency

Wang Wei-Tian, Yang Guang, Chen Zheng-Hao, Zhou Yue-Liang, Lü Hui-Bin, Yang Guo-Zhen
Chin. Phys., 2002, 11 (12): 1324-1327 doi: 10.1088/1009-1963/11/12/020
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Nanometre-sized gold particles embedded in BaTiO3 composite thin films (Au/BaTiO3) 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/BaTiO3 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.

Fragmentation of 16O nuclei in nuclear emulsion

Zhang Dong-Hai
Chin. Phys., 2002, 11 (12): 1254-1258 doi: 10.1088/1009-1963/11/12/007
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We present the topology of 16O 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.

Photon statistics of the micromaser with a Kerr medium

Wu Shu-Dong, Zhan Zhi-Ming, Jin Li-Xia
Chin. Phys., 2002, 11 (12): 1272-1275 doi: 10.1088/1009-1963/11/12/010
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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.

Carrier shock and frequency conversion of a few-cycle pulse laser propagating in a non-resonant two-level atom medium

Xiao Jian, Wang Zhong-Yang, Xu Zhi-Zhan
Chin. Phys., 2002, 11 (12): 1276-1279 doi: 10.1088/1009-1963/11/12/011
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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.

Scattering of protons and antiprotons by hydrogen atoms

Reda S. Tantawi, A.S.Sabbah
Chin. Phys., 2002, 11 (12): 1259-1266 doi: 10.1088/1009-1963/11/12/008
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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.

Molecular dynamics simulation for the sputtering of an Al2O3 sample bombarded with MeV Si ions

Xue Jian-Ming, Nobutsugu Imanishi
Chin. Phys., 2002, 11 (12): 1267-1271 doi: 10.1088/1009-1963/11/12/009
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Sputtering yield and kinetic energy distribution (KED) of Al particles from an Al2O3 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 Al2O3 target was developed, and both the nuclear energy loss Sn and electronic energy loss Se 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.

Fabrication and optical properties of platinum nanowire arrays on anodic aluminium oxide templates

Gao Tie-Ren, Chen Zi-Yu, Peng Yong, Li Fa-Shen
Chin. Phys., 2002, 11 (12): 1307-1312 doi: 10.1088/1009-1963/11/12/017
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Arrays of Pt nanowires, fabricated by electrodepositing Pt metal into nanoporous anodic aluminium oxide (AAO) templates, exhibit a preferable optical absorption band in the ultraviolet-visible (UV-VIS) spectra and present a blueshift as the wire aspect ratio increases or its radius decreases. This type of optical property of Pt nanowire/porous alumina composites has been theoretically explored using Maxwell-Garnett (MG) effective medium theory. The MG theory, however, is only applicable to nanowires with an infinitesimally small radius relative to the wavelength of an incident light. The nanowire radius is controlled by the pore radius of the host alumina, which depends on anodizing conditions such as the selected electrolyte, anodizing time, temperature and voltage. The nanowire aspect ratios depend on the amount of Pt deposited into the nanopores of AAO films. The optical absorption properties of the arrays of Pt nanowires with diameters of 24, 55 and 90 nm have been investigated by the UV-VIS spectra, which show that the extinction maximum (λmax) shifts to shorter wavelength side as the wire aspect ratio increases or its radius decreases. The results are qualitatively consistent with those calculated based on the MG theory.

Fractals in DNA sequence analysis

Yu Zu-Guo, Vo Anh, Gong Zhi-Min, Long Shun-Chao
Chin. Phys., 2002, 11 (12): 1313-1318 doi: 10.1088/1009-1963/11/12/018
Full Text: [PDF 257 KB] (Downloads:683)
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Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance, and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view) to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.

Social influence in small-world networks

Sun Kai, Mao Xiao-Ming, Ouyang Qi
Chin. Phys., 2002, 11 (12): 1280-1285 doi: 10.1088/1009-1963/11/12/012
Full Text: [PDF 226 KB] (Downloads:467)
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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.

Excitons in quantum-dot quantum-well nanoparticles

Shi Jun-Jie
Chin. Phys., 2002, 11 (12): 1286-1293 doi: 10.1088/1009-1963/11/12/013
Full Text: [PDF 263 KB] (Downloads:610)
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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 1se-1sh transition energies.

Study of ac hopping conductivity on one-dimensional nanometre systems

Xu Hui, Song Yi-Pu
Chin. Phys., 2002, 11 (12): 1294-1299 doi: 10.1088/1009-1963/11/12/014
Full Text: [PDF 248 KB] (Downloads:412)
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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.

Superconductivity and x-ray photoemission study of MgB2 thin films

Wang Shu-Fang, Zhou Yue-Liang, Zhu Ya-Bin, Zhang Qin, Xie Kan, Chen Zheng-Hao, Lu Hui-Bin, Yang Guo-Zhen
Chin. Phys., 2002, 11 (12): 1300-1302 doi: 10.1088/1009-1963/11/12/015
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Highly c-axis oriented MgB2 thin films with Tconset of 39.6K were fabricated by magnesium diffusing into pulsed-laser-deposited boron precursors. The estimation of critical current density Jc, using hysteresis loops and the Bean model, has given the value of 107 A/cm2 (15 K, 0 T), which is one of the highest values ever reported. The x-ray photoemission study of the MgB2 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.

A possible coupling mechanism between magnetism and dielectric properties in EuTiO3

Jiang Qing, Wu Hua
Chin. Phys., 2002, 11 (12): 1303-1306 doi: 10.1088/1009-1963/11/12/016
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The dielectric constant of an incipient ferroelectric EuTiO3 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 EuTiO3. We propose a possible coupling mechanism between the magnetic and electrical subsystems as -g\dsuml \dsum〈i,j〉q2l\vec Si·\vec Sj. 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.

Optically-thick accretion discs with advection

Chen Lin-Hong, Wu Mei, Shang Ren-Cheng
Chin. Phys., 2002, 11 (12): 1319-1323 doi: 10.1088/1009-1963/11/12/019
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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)RG where RG 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.
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