Dynamics of cubic-quintic nonlinear Schrödingeröequation are studied numerically with symplectic method. Behaviors of the equation are discussed with increased quintic nonlinear parameter. We observe homoclinic orbit crossing and elliptic orbit in turn and the system has recurrent solutions. Pattern drifting of solutions is also discussed. It is shown that pattern drifting can be slowed down by increasing the quintic nonlinear parameter.

With high order smooth non-uniform rational B-splines (NURBS) as basis function to simplify C¹ element construction, least squares isogeometric analysis is proposed for viscous incompressible Navier-Stokes equations. Governing equations are linearized by Picard or Newton method. Variational equation is derived from least squares functional defined by residuals of linearized equations. High order smooth finite dimensional spaces for velocity and pressure approximation are constructed by NURBS. Two benchmark flow problems were solved. Accurate numerical results were obtained for 2-dimensional lid driven flows. Global mass loss in flow past a cylinder in a channel decreased from 6% in classical least squares finite element method to 0.018%. It shows that the method is applicable to Navier-Stokes equations. It is better in mass conservation than least squares finite element method.

We investigate relaxation absorption of ultrasound and speed of sound dependence on temperature and constituent concentration of gas mixture.Two three-dimensional models,one based on molecular relaxation model and the other on sound velocity, are established for a sample consisting of carbon monoxide, nitrogen and oxygen.An algorithm is developed to reconstruct simultaneously temperature field,concentration field and flow of the mixture in sensing domain.Numerical simulation shows that the algorithm is feasible and applicable to measurement of complicated multi-physics fields.Errors arising in simulation are discussed.It is possible to use the algorithm for other component mixtures.

First principle calculations are made to study formation energies, partial DOS and magnetic moment of three typical surfaces of ZnS(001):Mn. Two interstitial locations are found more stable as comparing formation energies of Mn at three different locations on ZnS(001):Mn surface. Density of states and electron charge density of three reconstructions in ZnS(001):Mn surface are analyzed. It is found that p-d hybridization between spin up Mn-3d and S-3p orbital exists in three ZnS(001):Mn surface models. The p-d mixing is the strongest as Mn is at substituted location. Since spin down Mn-3d states are relatively local, it is shown that mixing between spin down Mn-3d and S-3p is less. Magnetic moments per supercell are calculated for three surfaces.

Classical trajectory method is used in 1D and 3D models to study classical dynamics of Hydrogen molecular ion (H₂⁺) in intense laser fields. Probabilities of survival, ionization, dissociation and Coulomb explosion and average distance between electron and the mass-center are calculated. It is shown that the 1D model is available for dynamics of hydrogen molecular ion in intense laser fields.

Classical trajectories of a diatomic molecule system (CO) in laser fields are calculated in the symplectic scheme. The calculated results are compared with that with Runge-Kutta (R-K) approach. The vibration trajectories, phase trajectories and vibration energy of a diatomic molecule CO are analysed.

An approach is proposed for producing a multi-colored noise from red noise to green one, and the correlation and spectral functions of this noise are given. It uses an integral-closed relation to simulate the multi-colored noise, and employs the Runge-Kutta algorithm to solve the Langevin equation itself. The average feature of the transport for a Brownian particle moving in a ratchet periodic potential is studied. The results show that the direction of the current driven by the green noise is opposite to the one driven by the red noise, and there is a noise with certain color which makes the current reversal.

A simple circuit model is presented for phase-shifted and single-longitudinal-mode distributed feedback semiconductor lasers. Th is model can be used for DC, AC and transient simulation. The simulated results with this model agree with the reports.

The continuation algorithm is applied to calculate the steady and periodic solutions of the 5-dimensional convection nonlinear dynamical system. The real bifurcation points curve, limit points curve and Hopf bifurcation points curve of the model are drawn in the parameter plane Ri-Re. The bifurcation diagram.is obtained. The different type of stable solutions such as stationary attractor, periodic attractor and chaotic attractor and so on exist in the different blocks or regions in the bifurcation diagram. Through analysing the bifurcation course of the steady and periodic solutions curve, the physical transitions both from steady state to periodic state and from periodic state to chaotic state which happened in the atomspheric stratified layer are discussed.The numerical computation results show that the continuation algorithm is a very effective computational method for researching into the bifurcation and dissipative structure of a nonlinear-dynamical system.

In this paper, a new method to determine the rate of Convergence of some terative methods for solving the systems of linear algebraic equations is proposed. The method is simpler and more effective than previons methods.It can show how the rate of convergence depends on some elements of the coefficient matrix of the system.Several iterative methods are considers and numerical results are given to illustrate our method and conclusions.