Table of contents

15 December 2001, Volume 10 Issue 12 Previous issue    Next issue

GENERAL

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THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS Bai Cheng-lin (白成林) Chinese Physics, 2001, 10 (12):  1091-1095.  DOI: 10.1088/1009-1963/10/12/301 Abstract ( 1173 )   PDF (212KB) ( 612 )   Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.

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KINETICS OF THE WAVETRAIN IN THE TWO-VARIABLE OREGONATOR MODEL Zhou Tian-shou (周天寿), Lü Jin-hu (吕金虎), Zhang Suo-chun (张锁春) Chinese Physics, 2001, 10 (12):  1096-1102.  DOI: 10.1088/1009-1963/10/12/302 Abstract ( 936 )   PDF (264KB) ( 383 )   In this paper we first discuss the asymptotic behaviours of solitary impulses in reaction-diffusion equations of Oregonator under the equal, single and double diffusion conditions, respectively. Then we obtain the asymptotic equations of motion of wavetrains for this model by a superposition of solitary impulses, and finally we analyse the stability of wavetrains.

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LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD Feng Shi-de (冯士德), Mao Jiang-yu (毛江玉), Zhang Qiong (张琼) Chinese Physics, 2001, 10 (12):  1103-1105.  DOI: 10.1088/1009-1963/10/12/303 Abstract ( 1047 )   PDF (244KB) ( 484 )   In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.

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CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION Feng Shi-de (冯士德), Ren Rong-cai (任荣彩), Cui Xiao-peng (崔晓鹏), Ji Zhong-zhen (季仲贞) Chinese Physics, 2001, 10 (12):  1106-1109.  DOI: 10.1088/1009-1963/10/12/304 Abstract ( 1025 )   PDF (221KB) ( 485 )   With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.

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NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS Liu Ke-jia (刘克家), He Li (何力), Zhou Guo-li (周国利), Wu Yu-jiao (伍玉娇) Chinese Physics, 2001, 10 (12):  1110-1112.  DOI: 10.1088/1009-1963/10/12/305 Abstract ( 962 )   PDF (201KB) ( 710 )   Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.

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SENSITIVE ERROR ANALYSIS OF CHAOS SYNCHRONIZATION Huang Xian-gao (黄显高), Xu Jian-xue (徐健学), Huang Wei (黄伟), Lü Ze-jun (吕泽均) Chinese Physics, 2001, 10 (12):  1113-1117.  DOI: 10.1088/1009-1963/10/12/306 Abstract ( 887 )   PDF (222KB) ( 619 )   We study the synchronizing sensitive errors of chaotic systems for adding other signals to the synchronizing signal. Based on the model of the Henon map masking, we examine the cause of the sensitive errors of chaos synchronization. The modulation ratio and the mean square error are defined to measure the synchronizing sensitive errors by quality. Numerical simulation results of the synchronizing sensitive errors are given for masking direct current, sinusoidal and speech signals, separately. Finally, we give the mean square error curves of chaos synchronizing sensitivity and three-dimensional phase plots of the drive system and the response system for masking the three kinds of signals.

ATOMIC AND MOLECULAR PHYSICS

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USING AN EVOLUTIONARY ALGORITHM BASED ON CELL DIVISION OPERATION TO CALCULATE GROUND-STATE ENERGIES OF DOUBLE-ELECTRON SYSTEMS IN MAGNETIC FIELDS Xu Jing-wen (徐静雯), Liu Lian-jun (刘莲君), Mao You-dong (毛有东) Chinese Physics, 2001, 10 (12):  1118-1123.  DOI: 10.1088/1009-1963/10/12/307 Abstract ( 1047 )   PDF (253KB) ( 331 )   In this paper we adopt a new approach---the evolutionary algorithm based on cell division operation－to deal with ground-state energies of double-electron systems. This algorithm is based on the evolution of sets and can incorporate other search algorithms. Firstly, we make a search for several good subsets of solution space at the same time. Then, we make a fine search in the neighbourhood of some better points obtained in the first step to determine the final optimal results. In addition, the cell division enables the solution subspaces to become smaller and smaller, and thus increase the convergence speed. We have tested this approach on double-electron systems in magnetic fields, and the results obtained have shown that it can improve not only the efficiency but also the accuracy of the calculations compared with other methods.

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DIELECTRONIC RECOMBINATION OF Co-LIKE Ag AND Ta IONS Yan Jun (颜君), Li Ping (李萍), Liu Chun-lei (刘春雷), Qiu Yu-bo (邱玉波), Fang Quan-yu (方泉玉) Chinese Physics, 2001, 10 (12):  1124-1128.  DOI: 10.1088/1009-1963/10/12/308 Abstract ( 1117 )   PDF (237KB) ( 539 )   Ab initio calculations of the rate coefficients for dielectronic recombination (DR) of Co-like Ag and Ta ions are performed based on Cowan's quasi-relativistic multi-configuration Hartree－Fock code. Co-like (3s 23p63d10)-1 configurations and Ni-like (3s23p63d10)-24l4l' autoionization configurations are included in the present calculation. Because of the extensive distribution of autoionization state energy levels, the DR rate coefficients cannot be reproduced or interpolated by a simple analytical formula, such as the Burgess－Merts formula, or the Hagelstein approximation. We propose to use multi-set Hagelstein parameters, which is convenient in practice and can reproduce well the ab initio calculated DR rate coefficients.

CLASSICAL AREAS OF PHENOMENOLOGY

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DESIGNING A DIFFRACTIVE OPTICAL ELEMENT FOR CONTROLLING THE BEAM PROFILE IN A THREE-DIMENSIONAL SPACE USING THE SIMULATED ANNEALING ALGORITHM Liang Wen-xi (梁文锡), Zhang Jing-juan (张静娟), Lü Jun-feng (吕俊峰), Liao Rui (廖睿) Chinese Physics, 2001, 10 (12):  1129-1135.  DOI: 10.1088/1009-1963/10/12/309 Abstract ( 1166 )   PDF (328KB) ( 576 )   We have designed a spatially quantized diffractive optical element (DOE) for controlling the beam profile in a three-dimensional space with the help of the simulated annealing (SA) algorithm. In this paper, we investigate the annealing schedule and the neighbourhood which are the deterministic parameters of the process that warrant the quality of the SA algorithm. The algorithm is employed to solve the discrete stochastic optimization problem of the design of a DOE. The objective function which constrains the optimization is also studied. The computed results demonstrate that the procedure of the algorithm converges stably to an optimal solution close to the global optimum with an acceptable computing time. The results meet the design requirement well and are applicable.

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CONTINUOUS-WAVE LASER OSCILLATION OF Yb:FAP CRYSTALS AT A WAVELENGTH OF 1043nm Yang Hui (杨辉), Zhao Zhi-wei (赵志伟), Zhang Jun (张军), Deng Pei-zhen (邓佩珍), Xu Jun (徐军), Wei Zhi-yi (魏志义), Zhang Jie (张杰) Chinese Physics, 2001, 10 (12):  1136-1138.  DOI: 10.1088/1009-1963/10/12/310 Abstract ( 1184 )   PDF (196KB) ( 431 )   A continuous-wave laser oscillation was demonstrated with a Yb-doped fluorapatite (FAP) crystal pumped with a 905 nm Ti:sapphire laser. The output characteristics for different output couplers were investigated. A maximum power of 67mW at a 1043nm wavelength was obtained with 10% output coupler, pumped by a Ti:sapphire laser with 910mW power. This corresponds to a slope efficiency of 26.5%.

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OPTICAL LIMITING EFFECT IN TWO PHTHALOCYANINES OBSERVED BY PICOSECOND PULSED LASER Qu Shi-liang (曲士良), Chen Yu (陈煜), Song Ying-lin (宋瑛林), Chen Guo-ping (陈国平), Wang Yu-xiao (王玉晓), Zhang Xue-ru (张学如), Liu Shu-tian (刘树田), Wang Duo-yuan (王夺元) Chinese Physics, 2001, 10 (12):  1139-1143.  DOI: 10.1088/1009-1963/10/12/311 Abstract ( 1057 )   PDF (236KB) ( 494 )   Optical limiting (OL) properties of two phthalocyanines were investigated by using picosecond laser pulses at 532nm. The relative ratios k of the absorption cross section of the first singlet excited state to that of the ground state were approximately obtained by the analysis of the experimental results in which the reverse saturable absorption model of the three-energy-level scheme was employed. A significant comparison with fullerene C60 was presented for OL. The OL mechanisms have been analysed in detail.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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EQUATION OF STATE OF FLUID He+H2 MIXTURES UNDER HIGH PRESSURE Chen Qi-feng (陈其峰), Cai Ling-cang (蔡灵仓), Sun Zhi-hong (孙志红), Jing Fu-qian (经福谦), Chen Dong-quan (陈栋泉) Chinese Physics, 2001, 10 (12):  1144-1148.  DOI: 10.1088/1009-1963/10/12/312 Abstract ( 1283 )   PDF (233KB) ( 462 )   A statistical mechanical variational theory and an improved van der Waals one-fluid model have been used to compute the equation of state of fluid He+H2 mixtures with different H2:He compositions under high pressure. The first-order quantum correction is included. Comparing the present results with Monte Carlo simulations indicates that the quantum corrections for calculating the thermodynamic properties become increasingly important at lower temperatures.

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

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LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS Chen Zhi-qian (陈志谦), Zheng Ren-rong (郑仁蓉) Chinese Physics, 2001, 10 (12):  1149-1153.  DOI: 10.1088/1009-1963/10/12/313 Abstract ( 1118 )   PDF (225KB) ( 667 )   In this paper we have calculated the variations of the gap $\Delta'(0,d)$ and transition temperature T'c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical dc, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'c decreases and $\Delta'(0,d)/k_{B}T'_{\rm c}\leq \pi e^{-\gamma}$ in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes $\Delta'(0,d)/k_{B}T'_{\rm c}> \pi e^{-\gamma}$  in even numbers of electrons.

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DYNAMICAL BEHAVIOUR OF THE SUPERCURRENT IN MESOSCOPIC JOSEPHSON JUNCTIONS Yu Kai-zhi (俞开智), Zou Jian (邹健), Shao Bin (邵彬) Chinese Physics, 2001, 10 (12):  1154-1156.  DOI: 10.1088/1009-1963/10/12/314 Abstract ( 1154 )   PDF (184KB) ( 466 )   In this paper we use a numerical method to study the quantum effect of dynamical localization on the supercurrent in a mesoscopic Josephson junction driven by a periodically external electromagnetic field. We find that the charge is localized effectively when the ratio of the field magnitude and the field frequency equal some critical values, and in these cases the amplitude of the oscillation of the supercurrent will remain constant.

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EFFECT OF $\alpha$-Fe SURFACE LAYER ON THE MAGNETIC REVERSION PROCESS FOR Nd2Fe14B CRYSTAL Zhao Su-fen (赵素芬), Jin Han-min (金汉民), Wang Xue-feng (王学凤), Yan Yu (闫羽) Chinese Physics, 2001, 10 (12):  1157-1162.  DOI: 10.1088/1009-1963/10/12/315 Abstract ( 1197 )   PDF (378KB) ( 500 )   The demagnetization process for a Nd2Fe14B grain covered by an $\alpha$-Fe layer was studied by use of the finite element technique of micromagnetics. $\mu$0iHc decreases with the increase of $\alpha$-Fe layer thickness t. With the increase of t from 0 to 6nm, $\mu$0iHc decreases from ～7 T to ～3.5 T when the angle between the applied field and the c-axis of the Nd2Fe14B grain is 0.5° and from ～4 T to ～1.5 T when the angle is 30° or 60°. The effect is only slightly affected by the angle between the $\alpha$-Fe layer and the field direction.

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DIRECT UPCONVERSION SENSITIZATION LUMINESCENCE OF Ho(0.1)Yb(5):OXYFLUORIDE VITROCERAMICS Chen Xiao-bo (陈晓波), Zheng Zhe (郑喆), Song Zeng-fu (宋增福) Chinese Physics, 2001, 10 (12):  1163-1168.  DOI: 10.1088/1009-1963/10/12/316 Abstract ( 924 )   PDF (236KB) ( 475 )   This paper studies the upconversion luminescence phenomenon of the Ho,Yb co-doped oxyfluoride vitroceramics. There is one group of strong upconversion luminescence lines positioned at 536.5nm, 18639cm-1; 540.5nm, 18501cm-1; 544.0nm, 18399cm-1, which is easily identified as the transitions of 5S2→5I8. There are other splendid upconversion luminescence lines, which are 5S2→5I7,5F5→5I8,5G6→5I8, (5G3G)5 →5I8,(3F3H5G)4→5I7,5G4→5I8 and (5G3H)5→5I8. It is also found that an interesting kind of upconversion cooperative radiation fluorescence comes from a kind of coupling state of clusters consisting of two Yb3+ ions.

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MAGNETIC VISCOSITY AND DEMAGNETIZATION BEHAVIOUR IN ISOTROPIC NANOCRYSTALLINE Pr12Fe82B6 RIBBONS Zhang Hong-wei (张宏伟), Zhang Shao-ying (张绍英), Shen Bao-gen (沈保根), D. Goll, H. Kronmüller Chinese Physics, 2001, 10 (12):  1169-1171.  DOI: 10.1088/1009-1963/10/12/317 Abstract ( 1062 )   PDF (207KB) ( 757 )   We present the experimental results of the magnetic viscosity, demagnetization curve and recoil loop for isotropic nanocrystalline Pr12Fe82B6 ribbons prepared by melt-spinning. The thermal fluctuation field, activation volume and irreversible demagnetization are discussed. The coercivity mechanism is mainly determined by the inhomogeneous nucleation rather than a simple nucleation of reverse domain.