We study ground states of a Bose-Einstein condensate in a harmonic plus Gaussian trap. It is found that as the condensate forms a giant vortex the number of vortices is equal to the average angular momentum and the density distribution of the ground state is the same as that of angular momentum. We draw a conclusion that the ground state with giant vortex is the eigen state of angular momentum. As the potential well changes from an isotropy toroidal trap to an anisotropic toroidal trap,the ratio of the average angular momentum of the condensates to the number of vortices decreases slowly from 1, and then drops rapidly and stays near 0.5. Characteristics of density distribution of condensate and angular momentum distribution are given and explanation is shown.

Thomas-Fermi approximation (TFA) and imaginary-time propagation method are used to study ground states of rotating Bose-Einstein condensates in an annular trap. Ground state density profiles of condensates experience a transition from vortex lattice phase to giant vortex phase with increase of angular frequency or with increase of width and center height of trap potential. Particularly, ground state density profiles change from a disc shape into an annulus shape with the increase of width and center height of trap potential, when angular frequency is zero. Finally, comparison between ground state density profiles, obtained by analytical method and numerical method is made. They coincide with each other.

We analyze numerically thermalization process of atoms sputtered from a cathode in N2/Ti micro-hollow cathode discharge plasma by using Monte Carlo method.PIC/MC model is used to simulate nitrogen ion(N₂⁺,N⁺) bombarding cathode surface.Thermalization process,density distribution and average energy of Ti atoms are calculated.It shows that initial energy sputtered to all directions from 90 percent of Ti metal atoms is less than 30 eV.Its scattering angle is mainly between 30 and 60 degrees.And thermalization maximum of sputtering Ti atoms is appeared at a distance of about 0.04mm from the hollow cathode wall.

Generation and properties of dark solitons are studied in detail by means of numerical simulation of quasi one-dimensional heteronuclear two-component Bose-Einstein condensates in syntonic potential. Dark solitons are only induced in one of the condensate components by modulational instability with instantaneous conversion of repulsive interspecies interaction to attraction. Solitons pass through each other periodically in syntonie potential. In addition, the number of dark solitons is affiliated with ratio of particle mass and ratio of particles numbers.

Development situations of domestic and overseas computational physics are discussed, such as society organizations, series of intermational conferences, corresponding institutes, university education and new developments in this field.From the above-mentioned developments, it is known that computational physics will have a flourishing development and a nice prospect in the 21st century.

A synthetic description on numerical methods is given for calculating periodic solutions of autonomous ordinary differentical equaitons.It focuses on the introductions of original structural ideas and processes of the methods or algorithms.

Energy cost that bounce shock wave on its propagation through outer iron core must pay for dissociation of heavy nuclei is considered as an adjusted parameter. Based on this, the method of artificial prompt explosion model is proposed to research effects of iron core mass of SN Ⅱ on prompt explosion. Range of iron core mass of presuperonva models which can produce prompt explosion is estimatd. The preliminary investsgation shows that iron core mass of presupermova models of WW(1993) is too large to produce prompt explosion.

The(0.74-0.91)M_⊙ of the iron core of Supernovae is a very important region of convective instability,which is found through the present numerical simulation.

This paper describes a new and pure Lagrangian method——called "Smoothed Particle Hy drodynamics" (SPH) method. The method is to actually evaluate spatial gradients without the use of any grid. Thus it does not suffer form the severe problems always associated with mesh tangling and distortion. Therefore it can be applied to multidimensional hydrodynamics which could effectively model three-dimensional systems which lack symmetry and possess large voids. At first, the paper gives an introduction to theoretical basis to SPH. Emphasis is given to a proper derivation of the SPH equations from the hydrodynamical conservation equations. Discussion covers some relative problems such as artifical viscosity, thermal conduction, self-gravity and sink and magnetic fields, choosing the smoothing kernels, and implementation of SPH code, etc.

In terms of the three basic forms and the eight-various cases of artifical viscosity for the same progenitor madel-"WW88", the numerical simulation has been performed for the whole processes of collapse and explosion of supernovae, and the artifical viscosity influences on compulation of supernovae explosion are investigated through analysis of numerical experimental results.

The objective of this study is to develop a mathematical model for calculating the initiation and spresd of fire resulting from an attack on an urban area, and to apply the model for predicting the fire-depentdent fire damage to an assumed city. The numerical test is obtained valuable information by using the parameters of fire spread from Japanese Hiroshima.The model to be developed is included——to determine description for a simplified urban,to take account of fire spread by radiation and firebrands in terms of statistical data, and to develop a computer program to perform the numerical simulation.

In this paper, we are devoted to a study of the effect of the treatment of Neumann boundary conditions for one-dimensional advection-diffusion equation by the analysis method, and for tow-dimensional Poisson equation by the numerical test method. The reults show that the scheme is first-order accurate in space (i.e. O(h)can be derived first-order accurate difference solution or second-order solution, and the O(h²) or O(h³) scheme is only derived second-order solution.

In this paper, we are concerned only with computer simulation of the fires of buildings ignited on urban areas produced by a nuclear burst. The numerical test is obtained sorne qualitative results for the simplest model by using the parameters of fire-spread from Japanese Hiroshima.

This paper is in order to solve the numerical computation of the periodic orbits of nonlinear autonomous differential equations. We design an optimal control method of the numerical computation. The solution method is basically a continue shooting method,under the guardianship of nonlinear least squaves that takes advantage of an optimal Central formulation, in which attached to the contral techniques of the penalty function.In this method,we use the Crank-Nicolson discretization schemes and Conjugate Gradient methods.This method has been applied to the solution of nonlinear differential equations modelling chemical reactions,the corresponding numerical results are presented here.

In this paper, we have designed the variational optimal algorithm, and used it to compute simultaneously the limit cycle and period of the Brussela-tor.

We take 15 M_☉ model of Weaver et al. as initial model,the collapse process of stellar core between the onset of collapse and core bounce has been calculated by using the eouation of state of us (EOSⅡ).With the simplified nuclear statistical equilibrium system mentioned above, the treatment of the thermal effects of neutronization, nuclear disintegration, nuclear combination and nuclear excitation has been attemped.The results of us are essential agreed with Van Riper's results.calculated by using the ILPR's equation of state for the same initial model.As the center density of core reaches 1014gcm-3, the maximum velocity of fall and the Ms (mass at sonic point)in model D is greater than that of the typical model of Van Riper by 2.7% and 7% respectively. In model D the neutrino trapping density is less than that of the typical model of Van Riper by 3% (at mass layer 0.15M_☉) but the lepton fraction in model D is greater than that of typical model of Van Riper by 8%(at 0.15M_☉) and by 10% (at 0.5M_☉).

In this paper, the properties of system consisting of various nuclear species and free nucleons are described by a nuclear statistical equilibrium system consisting of a typical heavy nucleus, a particles, free neutrons and protons.starting from a semiempirical expression for the mass of the heavy nucleus and the entropy (energy) of their excited states, an equation of state is developed by a restricted minimization of the total free energy of a fixed volume of matter at given temperature and electron fraction.his scheme gave good agreement with the equation of El Eid & Hillebrandt at density 10⁹-10¹²g cm^-3 and with lamb et al (ILPR's equation of state at density 10¹²-10¹⁴g cm^-3,ye=3,σ/k=1.5k.The imput physics such as the rate of electron capture on matter has been treated also more carefully.

For the computation of saturated-unsaturated water table flow, a kind of difference scheme of irregular convex polygon mesh is developed. Using this method, saturated-unsaturated seepage flow is calculated to AKAI's sand model and KOM-ADA's reservoir model. The results obtained here are compared with results ob -tained from computations in which rectangled difference meshes were used. The applicableness and accuracy of this method are also discussed.

For saturated-unsaturated water table flow, computations of ADEP, ADIP and implicitly alternating direction iterative procedure are made and compared.The i-terations are not convergent and computational results are strongly distortional Based on supplementing a particular term, a kind of completely implicit and altern-ting direction iterative procedure is given The relative results for computational model of different scales are satisfactory. Problems of how to give the particular supplemental term and how to select better parameters are discussed, the computational results are given.

The implicit alternating-direction-iteration method is used to solve question of saturated-unsaturated seepage flow under rapid change of the water surface level. The numerical.results of Akai model are given and compared with experimental results.It is found that the numerical results given in this paper are in good agreement with experimental results and better than results by finite element method.The numerical results of komada model are close to results by finite element method.