二维可积系统的求迹公式和周期轨道的量子化

从Berry–Tabor求迹公式出发,导出了二维可积系统周期轨道作用量的半经典量子化条件.利用此量子化条件,考虑周期轨道满足的周期条件,得到了二维无关联四次振子系统周期轨道作用量的半经典量子化条件,并给出了半经典能级公式.对能级与周期轨道的对应关系做了分析.     

两相壁面射流PDF方程有限分析方法及数值模拟

提出求解位置-速度相空间中高维两相流PDF(probability density function)方程的有限分析方法,将位置-速度相空间颗粒PDF方程约化到速度空间,并解析求解,颗粒的位置PDF用轨道方法求解.对壁面射流两相流动进行数值模拟,并与颗粒雷诺应力轨道方法进行比较计算,结果优于颗粒雷诺应力轨道方法.     

New High-Resolution Semi-discrete Central Schemes for Hamilton–Jacobi Equations

We introduce a new high-resolution central scheme for multidimensional Hamilton–Jacobi equations. The scheme retains the simplicity of the non-oscillatory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J. Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, independent of 1/Δt. By letting Δt↓0 we obtain a new second-order central scheme in the particularly simple semi-discrete form, along the lines of the new semi-discrete central schemes recently introduced by the authors in the context of hyperbolic conservation laws. Fully discrete versions are obtained with appropriate Runge–Kutta solvers. The smaller amount of dissipation enables efficient integration of convection-diffusion equations, where the accumulated error is independent of a small time step dictated by the CFL limitation. The scheme is non-oscillatory thanks to the use of nonlinear limiters. Here we advocate the use of such limiters on second discrete derivatives, which is shown to yield an improved high resolution when compared to the usual limitation of first derivatives. Numerical experiments demonstrate the remarkable resolution obtained by the proposed new central scheme.