A field method for integrating the equations of motion of mechanico--electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.     

The density wave in a new anisotropic continuum model

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

An extended master-equation approach applied to aggregation in freeway traffic

We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.     

Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilto-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.     

Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach （AMFP）. Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential （DE） model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.     

自喇曼散射及二阶色散系数对三阶飞秒孤子的影响

介绍了分步傅里叶数值方法的原理和步骤。通过数值模拟，得到随着自喇曼散射系数的增大，三阶飞秒孤子分裂的两个孤峰，左峰的超前越来越小，而右峰的延迟越来越大。从频谱上看，开始蓝移随着自喇曼散射系数的增大而增大，当增大到一定程度时，两边的频谱会中移。增加二阶色散系数，三阶飞秒孤子的裂化也会得到控制，在频域内表现为频谱中移变窄。     

A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations

In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.     

Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.