A numerical method based on integro‐differential formulation for solving a one‐dimensional Stefan problem

A numerical method based on an integro‐differential formulation is proposed for solving a one‐dimensional moving boundary Stefan problem involving heat conduction in a solid with phase change. Some specific test problems are solved using the proposed method. The numerical results obtained indicate that it can give accurate solutions and may offer an interesting and viable alternative to existing numerical methods for solving the Stefan problem. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Novel Gear-like predictor–corrector integration methods for molecular dynamics

A new class of predictor–corrector integration methods intended for molecular dynamics simulation is presented. The methods are derived from the original Gear methods by analysing the numerical solution of the harmonic oscillator. The corrector coefficients are chosen to improve the time-reversibility while keeping maximum stability. Tests performed on systems with forces not dependent on velocities (classical two-body problem and three simple atomistic systems) show good energy conservation and reduced deviations of measured quantities in comparison with the Verlet method. As regards the systems with velocity-dependent right-hand sides, a moderate improvement is found for the Nosé–Hoover thermostat but no improvement for fixed bonds constrained by the general constraint dynamics based on Lagrange multipliers.     

折反式大口径、大视场、宽光谱光学系统

在地面的目标探测光学系统多采用大口径(500 mm)同轴光学系统的前提下,系统探测的大视场和宽光谱就成了亟待解决的问题。设计了附带小口径球面透射校正镜组的折反式光学系统,利用该校正镜组校正了系统由于大相对口径、大视场和宽光谱带来的像差,使系统达到了预定的指标要求。其中只有主反射镜面形为二次非球面,设计参数也易于加工。在相应的实例要求下,用ZEMAX光学设计软件进行了优化评价,并给出了该系统的对星观测结果。该光学系统设计的口径为Ф750 mm,相对孔径为1:1.32,视场为4 ,光谱范围为500~800 nm,系统实际探测能力在15 Mv以上。该系统结构简单,均采用普通玻璃材料,成本低,成像质量良好。     

应用折-衍射元件校正人眼色差

提出了采用两个折射-衍射元件对人眼系统在14°范围内进行色差校正的光学系统设计方法。基于系统光学性能的评价与单片折射-衍射元件色差校正系统的对比验证了本文提出的色差校正系统的性能。结果表明：两种色差校正系统都可以很好地校正人眼的轴向色差。但是,单片折射一衍射色差校正系统引入了横向色差,其由校正前的14．51μm增加到81．4μm,严重影响了边缘视场处的成像质量。而采用双片折射一衍射元件的色差校正系统可同时对轴向色差和横向色差进行校正,使横向色差降为1．64μm。设计的色差校正系统可有效提高视网膜的成像质量,并可用于视觉仪器。     

Homogenization of the Maxwell Equations: Case I. Linear Theory

The Maxwell equations in a heterogeneous medium are studied. Nguetseng's method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.     

A staggered-grid numerical algorithm for the extended Boussinesq equations

A second-order accurate numerical scheme is developed to solve Nwogu’s extended Boussinesq equations. A staggered-grid system is introduced with the first-order spatial derivatives being discretized by the fourth-order accurate finite-difference scheme. For the time derivatives, the fourth-order accurate Adams predictor–corrector method is used. The numerical method is validated against available analytical solutions, other numerical results of Navier–Stokes equations, and experimental data for both 1D and 2D nonlinear wave transformation problems. It is shown that the new algorithm has very good conservative characteristics for mass calculation. As a result, the model can provide accurate and stable results for long-term simulation. The model has proven to be a useful modeling tool for a wide range of water wave problems.     

Viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow with diffusion

We establish viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed diffusion. The convergence is verified under various Sobolev norms, including the L^∞(H¹) norm.     

液晶自适应光学在天文学研究中的应用展望

液晶波前校正器作为一种高单元密度的新型波前校正器件,通过相息图的衍射可以轻松实现十微米的波前位相校正量。因此,基于液晶波前校正器的自适应光学(LCAO)系统是21世纪天文观测领域非常有希望普及的系统。但是液晶波前校正器存在响应速度慢(10ms)、能量利用率低的双重问题,国际上一直处于探索研究中。本课题组不但解决了能量问题,而且在速度方面不断取得进步,所研制的LCAO系统与1.23m口径望远镜连接,清晰观测到土星及其环绕的光环带,分辨出4.8和5.5视星等的α-Com双星,成像分辨率达到1.8倍衍射极限分辨率;目前系统延迟时间只有2ms,可以说已达到工程应用水平,在装备8~10m级大口径天文学望远镜方面极具应用潜力。     

An optimal error estimate for upwind Finite Volume methods for nonlinear hyperbolic conservation laws

The purpose of this paper is to show that the cell-centered upwind Finite Volume scheme applied to general hyperbolic systems of m conservation laws approximates smooth solutions to the continuous problem at order one in space and time. As it is now well understood, there is a lack of consistency for order one upwind Finite Volume schemes: the truncation error does not tend to zero as the time step and the grid size tend to zero. Here, following our previous papers on scalar equations, we construct a corrector that allows us to prove the expected error estimate for nonlinear systems of equations in one dimension.