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25 March 1994, Volume 11 Issue 1 Previous Issue    Next Issue

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INVESTIGATION OF NUMERICAL SIMULATIONS FOR LASER-PRODUCED X-RAY Zhang Jun, Chen Guangnan, Chang Tieqiang, Pei Wenbing, You Xiwen, Sui Chengzhi, Xu Shaoze, Gu Peijun, Zhang Shi, Zhang Xinghong 1994, 11(1): 1-8.  Abstract ( )   PDF (541KB) ( )   The paper presents the main processes of physics and the outline of the computational program related laser X-ray conversion, gives the typical pictures and numerical results. Based on numerical simulations, the laws of some important properies of physics are obtained, the results estimated by the scaling lasw are in comparison with the measurement values, they are coincident each other on quantitative tendency and quantitative results.

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NUMERICAL SOLUTION OF MELTING IN A RECTANGULAR ENCLOSURE WITH DISCRETE HEAT SOURCES Zhang Yuwen, Chen Zhongqi, Wang Qijie, Wu Qingjin 1994, 11(1): 9-16.  Abstract ( )   PDF (469KB) ( )   In order to simulate the cooling of electronic devices by solid-liquid phase change materials (PCM) the problem on two-dimensional melting heat transfer in a rectangular enclosure with discrete heat sources on one of its vertical walls has been solved numerically.Effect of Stefan number on the solid-liquid interfacial shape and wall temperature varition along the height of the wall are also discussed.

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A NUMERICAL METHOD FOR SINGULAR BOUNDARY VALUE PROBLEM FOR ORDINARY DIFFERENTIAL EQUATION He Qibing, Mou Zongze 1994, 11(1): 17-26.  Abstract ( )   PDF (531KB) ( )   A numerical method so called regularizing method applies for singular boundary value problem for ordinary differential equation with solutions that can be represented as series expansions on a subinterval near the singularity. A regular boundary value problem is derived on thd remaining interval, for which a difference method is used. Convergence results and numerical examples are given.

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IMAGE RECONSTRUCTION VIA “SQUASHING” IN THE BOREHOLE ELECTROMAGNETIC WAVE TECHNIQUES Yao Yun, Guo Ping 1994, 11(1): 27-34.  Abstract ( )   PDF (430KB) ( )   In the borehole electromagnetic wave techniques exist problems on "Image reconstruction from incomplete projections data", The problems can be treated via "Squashing".Image reconstruction via "Squashing" with physical models is discussed and calculation results are better.

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THE CALCULATION OF SHORT RANGE ORDER IN NEMATIC LIQUID CRYSTALS Zhang Zhidong, Yang Guochen 1994, 11(1): 35-37.  Abstract ( )   PDF (194KB) ( )   Some important physical effects appear due to short range order in nematic liquid crystals. On the basis of the cell theory, new numerical method is presented, which are used to calculate these effects.We do not use ann functional expansions but we obtain accurate orientational distribution functions by solving the equation of equilibrium state, using an iterative method. Then various physical quantities can be calculated. The accurate numerical results of order parameter at phase transition and entropy change etc. are given.

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OPERATOR-SPLITTING MATCHED ARTIFICIAL DISPERSIVITY METHOD IN SOLVING THREE-DIMENSIONAL ADVECTION DOMINANT ADVECTION-DISPERSION PROBLEMS Zhang Zhihui, Xue Yuqun, Xie Chunhong, Wu Jichun 1994, 11(1): 38-44.  Abstract ( )   PDF (439KB) ( )   A new method is presented to solve the three-dimensional advection dominant advection-dispersion equation, in which not only the advective-dispersive actions, but also the adsorption,radioactive decay and sources(sinks) are considered. Operator-splitting(OS) technique is used to split the equation over a time step into three parts, which are respectively solved by the method of constant variation (CV), the matched artificial dispersivity (MAD) method and the alternating direction implicit (ADI) method. Finally, the new method is applied to a synthetic three-dimensional contaminant transport problem. The simulated results are satisfactory by comparison with the analytical and the improved characteristic (IC) method solutions.

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CONSTRUCTION OF SYMMETRIC TVD SCHEMES AND THEIR APPLICATIONS Lu Xiyun, Zhuang Lixian, Tong Binggang 1994, 11(1): 45-50.  Abstract ( )   PDF (336KB) ( )   A class of second-order explicit and implicit symmetric total variation diminishing (TVD) schemes is constructed for the computation of weak solutions of hyperbolic conservation laws.The resulting scheme can be viewed as a limited anti-diffusive flux, that is centered weighted flux, to add to a first-order GCIR scheme. Numerical experiments for solving the Euler equations for capturing shock waves show that the symmetric TVD schemes are quite robust and accurate.

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APPROXIMATE SOLUTION FOR NLS EQUATION OF INCLUDING RAMAN EFFECT Shen Tinggen, Yan Zhongqiang 1994, 11(1): 51-58.  Abstract ( )   PDF (451KB) ( )   In this paper the approximate solution for NLS equation, including Raman Effect,by using common mathematics is given, and the Raman effect in the solution of the NLS equation is discussed in detail.

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AN UPWIND FEM SCHEME FOR ELECTROMAGNETIC FIELD PROBLEM IN MOVING MEDIA Shen Ming, Shi Zhanwei 1994, 11(1): 59-67.  Abstract ( )   PDF (462KB) ( )   An upwind scheme for periodic electromagnetic field problems in moving media is developed in the paper. When the Peclet number of discrete grid is larger than one, the procedure using Galerkin method will provide spurious oscillations in the computed results. To suppress these oscillations, an upwingd finite element method with two different upwind parameters in upwind and downwind sides is introduced. To one dimensional problems, this method can provide nodally exact solution for even spacing grids. Based on the one dimensional result, a cooresponding two dimensional scheme is suggested and tested by a 2-D model.

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FORECAST INTERFACES BEFORE THE TUNNEL FACE BY COMPUTER TOMOGRAPHY Chen Licheng, Xu Bangbao, Wang Dawei, Wang Molin 1994, 11(1): 68-74.  Abstract ( )   PDF (702KB) ( )   The theoretic model: there are three interfaces before the tunnel face,the medium between any adjacent interfaces is homogeneous and the wave velocity in one layer of medium may be different from ones in the others.We studied the methods of forecasting,layer by layer,and reversed the arrival time of wave which deduced by the known interfaces and wave velocities to the interfaces. Results are almost concordant with the fact.To the tunnel model and Yuntai Mountain tunnel face, we recorded waveforms respectively by ultrasonic detector and seismic detector. By analysis of severel of waves on record, we obtained the data on the arrival time of the reflection wave, and then reversed the data to the interfaces.The results are in good agreement the true conditions.

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A HIGH PRECISION COMBINATION METHOD OF NYSTR?M APPROXIMATIONS FOR SOLVING THE BOUNDARY INTEGRAL EQUATIONS OF THE SECOND KIND Lü Tao, Ma Chang zheng 1994, 11(1): 75-84.  Abstract ( )   PDF (542KB) ( )   A high pricision combination method for solving BIE of the second kind is presented. The combination algorithm is as follows:Step 1. Compute the jth(j=1,…,m) Nyström approximate equation with nodes {(nj+j)/(mn)}i=1n parallelly. Step 2. Compute the jth(j=1,…,m) interior print value by the jth Nyström solution parallelly. Step 3. Compute the average of m interior point values, which is the combination approximation.It can be proved that the precision of the combination approximation is almost same as the precision of Nyström appximation with mn nodes.

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A KIND OF EXPLICIT SCHEME WITH ARBITRARY STABILITY CONDITION FOR DISPERSION EQUATION Zhang Dakai 1994, 11(1): 85-90.  Abstract ( )   PDF (311KB) ( )   A kind of three level explicit difference scheme with two parameters m and θ,including four knots in the middle level is presented, for the dispersion equation ur=auxxx.When the m and θ satisfy a certain ralation, the stability condition is |γ|≤(m+1)/(4(m-1))(|m|>1).Thus, as m goes sufficiently neer to 1, an arbitrary stability condition can be obtained, and the order of the truncation error is not changed. The numerical example verifies the results of the theoretical analysis.

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RELATIVISTIC CALCULATION OF ENERGY LEVELS AND OSCILLATOR STRENGTHS FOR NEON-LIKE TITANIUM IONS Li Yueming, Li Shichang, Yang Hanyang, Sun Yongsheng, Han Guoxing 1994, 11(1): 91-101.  Abstract ( )   PDF (587KB) ( )   The GRASP program based on the multi-configuration Dirac-Fock self-consistent method have been extended and revised, so 15 configurations which consist of 89 energy levels in Ne-like titanium ions can be calculated in the same self-consistent process.In the calculations, the averaged level (AL) model and the Fermi two-parameter distribution model of the nuclear volume effect are considered, also Breit correction, vacuum polarization and self-energy effect are counted. LS and jj coupling labels are determined by the maximum combination coefficients. Electric dipole, electric quadrupole and magnetic dipole transition probabilities and oscillator strengths are calculated. The results of oscillator strengths are given in both the Coulomb and the Babushkin gauge, and the electro-dipole oscillator strengths in Babushkin gauge are also compared with the nonrelativistic counterpart.

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WAVE EQUATION NUMERICAL MODELING OF HEXAGONAL SAMPLE BY FOURIER METHOD Yao Dezhong, Ruan Yingzheng, Liu Guangyuan 1994, 11(1): 102-106.  Abstract ( )   PDF (312KB) ( )   The wave equation initial value problems are solved numerically on the grid of hexagonal sample by fourier method. A numerical test by this approach shows the availability and the efficiency over the rectangular sample.

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REAL-SPACE RENORMALIZATION GROUP APPROACH TO QUASI-PERIODIC LAYERED FERROMAGNETIC/SUPPERLATTICES Liu Tianshi, Wei Guozhu 1994, 11(1): 107-112.  Abstract ( )   PDF (305KB) ( )   The real-space renormalization group approach is used for quasi-periodic layered ferromagnetic super lattice in which a site with spin sa or sb,between layers the exchange energy are J1 and J2, which are arranged in quasi-periodic Fibonacci sequence, and exchange energy J0 in each layer. When J1=J2=J0, we obtained an exact decimation transformation for local magnons of layers α,β(γ) and б(τ)in the ferromagnets. Iteration of the transformation provides numerical results for the local density of states (LDOS) and the magnetization. We found the band widthes of LDOS of layers depend on J1, J2, sa adn sb.

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THE CALCULATION OF CRITICAL PARAMETERS FOR THE SITE PERCOLATION PROBLEM BY MONTE CARLO RENORMALIZATION GROUP Yang Jing, Yang Zhubao, He Yancai 1994, 11(1): 113-118.  Abstract ( )   PDF (394KB) ( )   The percolation threshold and critical parameters are obtained for the site-percolation problem on the square lattice with next-nearest-neighbour interactions by using Monte Carlo position space renormalization group procedure.It is shown that the site percolaton problems on the square lattice with next-nearest-neighbour interactions belongs to the same universality class as that with nearest-neighbour interactions.

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A NUMERICAL ITERATIVE METHOD FOR THE INVERSE PROBLEM OF 2-D WAVE EQUATION Cong Wenxiang 1994, 11(1): 119-122.  Abstract ( )   PDF (216KB) ( )   A new iterative method is proposed for the inverse problem of 2-D acoustic equation. As a kind of Newton-type iteration, the method overcomes the ill-posed of inverse problem by Tikhonov's regularization method in each iterative step and has a good numerical stability.The Numerical results show that this method is feasible and effective.

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MATHELDCA-A MATHEMATICA PROGRAM FOR CALCULATING ONE LOOP FEYNMAN DIAGRAMS WITH AMPLITUDES Ma Wengan, Sun Lazhen, Chen Xiaoxi, Qian Minglun 1994, 11(1): 123-128.  Abstract ( )   PDF (342KB) ( )   Using Mathematica symbalic manipulation system, the computer program MATHELDCA is developed for calculating one loop Feynman diagrams in renormalizable gauge theories. It is only needed to input the amplitudes of contributed diagrams according to the Feynman rule, so as to calculate the radiative corrections of particle process.