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25 May 1999, Volume 16 Issue 3 Previous Issue    Next Issue

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An automatic differentiation technique: differential algebra and its application in charged particle optics Wang Liping, Tang Tiantong 1999, 16(3): 225-234.  Abstract ( )   PDF (369KB) ( )   Differential algebra is a new mathematical method and a promising tool in charged particle optics. As a kind of automatic differentiation techniques, it is based on the nonstandard analysis and normal power series theory. It presents a straightforward method for the study of arbitrary order property of nonlinear systems, with accuracy limited only by the computer. The differential algebraic method is widely applicable, and it is an effective and elegant tool for the tracking, analysis and correction of high-order aberrations, sensitivity analysis and optimization of structure design, etc., of the charged particle optical systems. The principle and virtues of differential algebra are summarized. The application of differential algebra method in charged particle optics and its implementation in various computer languages are analysed. Some new research subjects in this field are discussed.

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Inverse problem of boundary incident radiation heat flux in semitransparent planar slab Liu Linhua, Tan Heping, Yu Qizheng 1999, 16(3): 235-242.  Abstract ( )   PDF (305KB) ( )   The coupled heat transfer processes of radiation, conduction and convection in semitransparent planar slab are analyzed. An inverse method is presented for estimating the unknown boundary incident radiation heat flux in semitransparent planar slab with transparent boundaries from the knowledge of the radiation intensities exiting the boundaries. The effects of anisotropic scattering, absorption coefficient, scattering coefficient, fluid temperature outside the boundaries, convection heat transfer coefficients, conduction coefficient of semitransparent media and slab thickness on the accuracy of the inverse analysis are investigated. The results show that this method is praticable.

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Mathamatical study on semi-langrangian advection computational scheme Wang Bizheng 1999, 16(3): 243-252.  Abstract ( )   PDF (350KB) ( )   Mathematical study on semi_Lagrangian advection computational scheme is carried out. Firstly, by the characteristic curves of the partial differential equation of first order, the existence and the uniqueness of the characteristic curves are proven. Secondly, by Picard's and В. Канторович's mechods, the search for the departure point is sloved systematically. At the end, from differential and computational geometry, one_dimensional shape perserving interpolation on the basis of non_linear spline is proposed, and two dimensional shape perserving interpolation on the basis of Lagrangian, bicubic spline and Coon's surfaces is introduced.

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Numerical calculation of full waveform acoustic logging in transversely isotropic porous formation Zhang Chengguang, Liu Yinbin, Che Wenhua 1999, 16(3): 253-258.  Abstract ( )   PDF (271KB) ( )   Based on the generalized Biot's theory in anisotropic porous formation and Kuijian's theory of multipole acoustic logging, full waveform acoustic logging in transversely isotropic porous formation is discussed. The monopole and dipole acoustic logging full waveforms are numerically calculated using the extended dynamic permeability given by Johnson et al. The results show that the horizontal permeability is closely related to the acoustic logging waveforms.

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The study of the coaxial reditron by means of computer simulation Hu Hongqing, Yang Zhonghai 1999, 16(3): 259-264.  Abstract ( )   PDF (342KB) ( )   The coaxial Reditron (the reflected electron discrimination tube) is investigated by means of the two-and-one half-dimensional fully electromagnetic model's particle-in-cell simulation.The results of simulation indicate that the oscillation of virtual cathode will be formed in coaxial guide when the current above the space-charge-limiting current is injected.For the given simulation's parameters,the highpower,narrow band,TM01 mode's microwave can be generated.The peak value of instantaneous output power is 8.62 GW with efficiency of 7 to 10 percent.

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Numerical simulation of premixed turbulent reacting flow in a sudden expansion combustor Zhang Jian, Zhou Lixing 1999, 16(3): 265-270.  Abstract ( )   PDF (227KB) ( )   The premixed turbulent reacting flow in an axisymmetric sudden-expansion combustor has been numerically simulated. The k-ε turbulent transport model and the EBU-Arrhenius turbulent reaction model are utilized for the closure of the time-averaged governing equations. The calculated results cover the time-averaged gas flow field, species mass fraction and temperature distributions for the premixed reacting flow in the sudden-expansion combustor. The EBU-Arrhenius model is discussed and evaluated based on the comparisons between the calculated results and the measured data.

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Mutual synchronization of the coupled map lattices Liu Zonghua, Chen Shigang 1999, 16(3): 271-278.  Abstract ( )   PDF (342KB) ( )   The nonlinear interaction of two coupled lattice dynamical systems is investigated. It results in identical synchronization when the two coupled lattice systems are same and in generalized synchronization when the parameters are different or the two coupled lattice systems are different. The largest Lyapunov exponent spectra are calculated.

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The estimation of ‖ Rp ‖ ∞ and condition number for high order iccg method Lei Guangyao, Huang Chaohui 1999, 16(3): 279-285.  Abstract ( )   PDF (253KB) ( )   Using the method of high order approximate LU dicomposition, the preconditioning matrices of high order ICCG are given and the ‖Rp‖∞ is also estimated when P=3 and 4. The upper bounds of Cond (LPUP)-1A for P=3 and 4 are obtained respectively. For different mesh sizes, the computed results of Cond (LPUP)-1A are also compared with the theoretical upper bound.

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A new finite difference method for solving initial boundary value problem of a nonlinear klein gordon equation Zhang Luming, Chang Qianshun 1999, 16(3): 286-294.  Abstract ( )   PDF (308KB) ( )   A finite difference of energy conservation is proposed for nonlinear Klein Gordon (NKG) equation.Its convergence and stability have been proved.Results of numerical computation are also analysed.

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The solution of compressible stability equations and forecasting of transition Yao Wenxiu, Cai Chunpei, Zhao Lie, Wang Famin, Zhao Guiping 1999, 16(3): 295-301.  Abstract ( )   PDF (279KB) ( )   It assesses the Rayleigh inverse-iteration method and boundary layer asymptotic expansion method, and uses them into the stability equations of compressible boundary layer and the numerical method for forecasting the transition point. It gives also a stability analysis on the first mode of the boundary layer of flat plane and a forecasting of transition point. Results are discussed and compared with observations.

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Numerical simulation of transient conjugate heat transfer with internal heat sourcesa Jiang Peixue, Ke Daoyou, Ren Zepei 1999, 16(3): 302-308.  Abstract ( )   PDF (371KB) ( )   Conjugate heat transfer of transient thermal conduction,natural convection and thermal radiation with internal heat sources is simulated numerically using PHOENICS(Version 1.4) with the false density method.The flow field and temperature distribution are calculated using both the body fitted coordinates and Cartesian coordinates.The variation of the maximum temperature in the substance with internal heat sources is presented as function of the environmental temperature.

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Computing fractal dimension and the kolmogorov entropy from chaotic time series Zhao Guibing, Shi Yanfu, Duan Wenfeng, Yu Huarui 1999, 16(3): 309-315.  Abstract ( )   PDF (279KB) ( )   On the basis of the G-P algorithm it proposes an optimal algorithm for computing simultaneously the correlation dimension and the Kolmogorov entropy from time series.The correlation dimension obtained from this method is optimal and the stable estimation of the Kolmogorov entropy is also obtained.The applicability of the method is illustrated with two examples,viz.,the Lorenz attractor and Rossler attractor.

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Calculation of the action of static electric field on SmC* liquid crystals Qian Xiangzhong 1999, 16(3): 316-320.  Abstract ( )   PDF (196KB) ( )   The effect of static electric field in smectic layer plane on the helic structure and ferroelectrics of SmC* liquid crystals is studied by the self-consistent simulation method. The results show that the helic pitch and the average of polarization increase with field strength, the closer to the threshold field, the faster they increase, the tilt angle of director and molecular orientional order parameter increase slowly with field strength and the threshold field decreases with temperature and is related to the helic pitch and polarization without external field.

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Quantum fluctuation under squeezed vacuum state and influence of source on the fluctuation in a mesoscopic coupled circuit Cui Yuanshun 1999, 16(3): 321-327.  Abstract ( )   PDF (250KB) ( )   The energy spectra of coupled circuit are given, quantum fluctuations of charge and current under the squeezed vacuum state and influences of source on the fluctuation in a mesoscopic circuit are investigated by quantizing an active non-dissipation mesoscopic coupled circuit and diagonalizing its Hamiltonian.

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The calculation of atomic parameters for coi-like ions 3p63d9,3p53d10 and 3p63d84p configurations Chen Minglun, Ji Shiyin, Fan Jinhua, Gong Lunxun, Mo Zhouwen, Yu Zhengguang, Li Xiaochang, Yang Xiangdong 1999, 16(3): 328-332.  Abstract ( )   PDF (205KB) ( )   The energy level、wavelength and Oscllatar strength for Highly ionized NiI-like ions 3p63d9,3p53d10 and 3p63d84p configurations are calculated by using Cowan's multiconfiguration selfconsistent field method together with the fitting formula proposed here.

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Calculation of energy exchanging term between electron and radiation in three temperature equations Pei Wenbin, Chang Tieqiang 1999, 16(3): 333-336.  Abstract ( )   PDF (157KB) ( )   The energy exchanging term between electron and radiation often makes the three temperature energy equations stiff at Te~Tr region and causes difficulty in numerical simulation of laser-target coupling.In near local thermodynamic-equilibrium (LTE) region,the emission and absorption of radiation are large and nearly equal,which results in divergence of iteration.In order to solve this problem,this paper discusses a method in which different expressions of the energy exchanging term in non-LTE and nearly LTE regions are given.The energy exchange in near LTE case has been calculated by using Rossland mean free path,instead of bound electron population.