Two-Dimensional Riemann Problems for the Compressible Euler System

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. The author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems, to illustrate their worthiness. Two-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics; that is, simplified model is built via asymptotic analysis, numerical simulation and theoretical analysis. A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic process. State-of-the-art numerical methods in numerical simulations are used to discern smallscale structures of the solutions, e.g., semi-hyperbolic patches. Analytical methods are used to establish the validity of the structure revealed in the numerical simulation. The entire process, used in many of Majda＇s programs, is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws     

凸四边形上一类具有C~2-连续的插值问题的样条解及其应用

本文讨论了一类凸四边形上的插值问题.指出这类插值问题是可解的,其解是分片二元三次多项式,且在凸四边形上是C~2-连续的.我们证明了这类插值问题的解的存在性和唯一性,给出了解样条的分片表达式及其逼近度的估计.最后还给出了一个应用实例和图形显示来说明本方法是可行的.     

A Dinuclear Cu(Ⅱ)-based Coordination Framework with Two-fold Interpenetrated 3D pcu Topology Displaying Catalytic Activity

A new Cu(Ⅱ) coordination polymer, [Cu2(mip)2(bmix)]n(bmix = 1,4-bis(2-methylimidazole-1-ylmethyl)benzene, H2 mip = 5-methylisophthalic acid), has been hydrothermally synthesized and characterized by elemental analyses, IR, TGA and single-crystal X-ray diffraction. The title compound belongs to the triclinic system, space group P1 with a = 9.435(5), b = 12.241(6), c = 13.666(6), β = 94.396(8)o, V = 1565.5(13) 3, Z = 2, C34H30Cu2N4O8, Mr = 749.70, Dc = 1.590 g/cm3, μ = 1.419 mm-1 and F(000) = 768. The title metal-organic coordination polymer exhibits the first two-fold interpenetrated pcu topological structure assembled by two types of dinuclear copper(Ⅱ) clusters and a flexible bis(imidazole)-based ligand. In addition, the fluorescence and catalytic performances of the complex for the degradation of Congo red azo dye in Fenton-like process were presented.     

激光投影显示中光棒匀光的照明光路设计

在方棒照明系统的基础上,根据激光光源的发光特性和准直性,设计了一款用于激光投影显示的,基于光棒匀光的照明光路系统。此系统具有结构简单、开发周期短、加工成本低的优点。仿真结果表明:设计的激光投影机光能量利用率达到78%,均匀度达到85%,满足激光投影显示中对集光和照明的设计要求。     

灰度调整与数字全息图像质的关系

如何在有限的灰度级别下输出高质量全息图是人们关注的问题之一.文章从数字全息图 （计算机制全息图）的灰度直方图出发,研究灰度调整对全息图再现像质的影响.首先通过理论推导研究了压缩计算机制全息图中占比例少的灰度,展宽占比例多的灰度后全息图衍射效率的变化,发现处理后的计算机制全息图经灰度压缩的阈值越大,衍射效率越高.然后研究了灰度压缩的阈值对计算机制全息图再现像噪音的影响,发现全息图再现像的噪音随着阈值的增大,先减少再增大.实验表明,通过取合适的阈值对全息图进行灰度调整,可以在保证全息图再现像的信噪比的同时,提高全息图的衍射效率.计算机仿真和全息图光学再现实验证明了理论分析是正确的,为制作高质量的计算机制全息图提供了参考依据.     

基于视场拼接的全视差三维显示系统

提出了一种新的基于视场拼接的全视差三维显示方法及图像生成方案.系统核心部分由一个微投影机阵列、一个反射光路和一个散射屏组构成,图像生成方案采用基于OpenGL的算法实现.为了验证所提出的基于视场拼接理论的正确性,利用液晶显示器、菲涅耳镜组、定向散射屏和背投式反射光路搭建了实验样机.该装置可以在更紧凑的系统结构下显示包括横向视差和纵向视差在内的三维图像,并且通过图像生成算法的配合实现了动态三维显示效果.     

The Interaction of Peregrine Solitons

We theoretically investigate the interaction of two in-phase and out-of-phase Peregrine sofitons in a Kerr nonlinear medium, addressing both the cases of first- and second-order solitons. Upon adjusting the interval between the sofitons, their interactions exhibit different properties. If the interval is sufficiently large, two Peregrine sofitons will propagate individually and will not interact each other. However, if the interval is not very large, the Peregrine solitons will strongly interact and display varying behavior.     

Above-Threshold Ionization of Xenon by Chirped Intense Laser Pulses

We experimentally investigate above-threshold ionization of xenon subject to chirped intense laser pulses. While for few-cycle laser pulses free of chirp, the Freeman resonance narrow peaks in the photoelectron spectra become strongly suppressed, they will re-emerge for laser pulses with a certain chirp. Moreover, the position of the resonant peaks exhibits a strong dependence on the direction of the chirp. The experimental features can be understood by a two-step ionization process; that is, a multi-photon excitation plus subsequent ionization process.     

Electron Dynamics of Atoms in Parallel Electric and Magnetic Fields

Through an analysis of the nearest neighbor level fields, we investigate the evolution of the electron spacing statistics for atoms in parallel electric and magnetic dynamics as electric field strength increases. In the ＇inter-l mixing＇ predominant region, the electron shows complex dynamics while in the ＇inter-n mixing＇ predominant region, its dynamics behaves in a relatively stable way and the characteristic quantity ξ shows a slight oscillation. Comparing the dynamics for hydrogen and barium, we find that the core effect makes the main contribution to the chaotic behavior in non-hydrogen atoms.