Scattering states of modified PSschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

Application of dual reciprocity boundary element method for prediction of acoustic characteristics of ducts and silencers with three-dimensional potential flow

The Dual Reciprocity Boundary Element Method （DRBEM） is applied to predict the acoustic characteristics of ducts and silencers with three-dimensional potential flow, and the basic principle and numerical procedure of the proposed method are introduced. Compared to the Conventional Boundary Element Method （CBEM）, the DRBEM takes into account the second order terms of flow Mach number in the acoustic governing equation, which is suitable for the situations with higher Mach number subsonic flow. The four-pole parameters of a duct and a varying cross-sectional area expansion chamber are predicted with the DRBEM, and the predictions are compared with the one-dimensional analytical solutions and the CBEM results. The comparisons demonstrated that the present method is valid. Transmission loss of silencers with different structures was also calculated with the DRBEM. The results showed that the influence of the three-dimensional flow on the acoustic characteristics of silencers with complex structures is not negligible.     

Scattering states of modified Pöschlben Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term, and apply this new approach to the Schrödinger equation with the modified Pöschl-Teller potential in the D-dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method (APM).     

Parameter design of a liquid-filled sloshing system

<正>The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis,the analytical expressions of the solutions of this kind of system are obtained.With different parameters,the dynamical behaviors of the solutions are different from the trivial ones.To prevent system instability,two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given.Meanwhile,numerical simulations are also given,which confirm the analytical results.     

Approximate solutions of SchrSdinger equation for Eckart potential with centrifugal term

The approximate analytical solutions of the Schrodinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ= λ=1, and β=0, are investigated.     

First and Second Sound Modes in a Uniform Fermi Gas

First and second sound modes in a uniform fermionic atom gas with Feshbaeh resonance are investigated in the frame of a two-fluid model at finite temperature. All thermodynamic quantities axe calculated for a given thermodynamic potential. The analytical results for thermodynamic quantities and sound velocities in BCS and BEC limits are obtained. The numerical results show that there exists a continuous interpolation for sound velocities of the first and second sound modes at fixed T/Tc between BCS and BEC limits. The existence of the second sound mode indicates the existence of superfluidity.     

Approximate solutions of Schrdinger equation for Eckart potential with centrifugal term

The approximate analytical solutions of the Schrdinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.     

A numerical study of a turbulent mixing layer and its generated noise

A direct numerical simulation of a turbulent mixing layer with the Reynolds number 500 and the convective Mach number 0.6 is performed and the results obtained are used to study the turbulent flow field and its generated noise.In the present simulation,the numerical techniques of absorbing buffer zones,artificial convection velocity and spatial filtering are used to achieve nonreflecting boundary conditions.The self-similarity is used to validate the present numerical simulations.The large-scale coherent structures are plotted together with the acoustic waves,which demonstrates the directivity of acoustic waves.The Lighthill’s source and space-time correlations are further investigated.The main contributions to mixing noise are identified in terms of large-scale coherent structures,Lighthill’s source and space-time correlations.     

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method (RKPM), a new meshless method, which is called the complex variable reproducing kernel particle method (CVRKPM), for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.