Traffic noise and the hyperbolic plane

We consider the problem of sound propagation in a wind. We note that the rays, as in the absence of a wind, are given by Fermat’s principle and show how to map them to the trajectories of a charged particle moving in a magnetic field on a curved space. For the specific case of sound propagating in a stratified atmosphere with a small wind speed, we show that the corresponding particle moves in a constant magnetic field on the hyperbolic plane. In this way, we give a simple ‘straightedge and compass’ method to estimate the intensity of sound upwind and downwind. We construct Mach envelopes for moving sources. Finally, we relate the problem to that of finding null geodesics in a squashed anti-de Sitter spacetime and discuss the SO(3,1)×R symmetry of the problem from this point of view.     

辛几何算法在计算非磁化等离子体中波传播轨迹时的应用

为了在数值计算中保持哈密顿系统的辛几何结构不变,利用辛几何算法得到了在线性哈密顿系统中射线追踪方程的一般辛差分格式。通过具体算例,利用辛几何算法计算了波在非磁化等离子体中的传播轨迹,并且与传统Runge-Kutta-Fehlberg算法所得结果进行了比较。利用辛几何算法所得传播轨迹与解析解一致,其色散函数值的误差随时间线性增长,能在长时间内保持色散函数值在一个很小的误差范围内。利用传统的Runge-Kutta-Fehlberg算法所得传播轨迹与解析解不一致,其误差随时间做大幅振荡增加。计算结果表明辛几何算法在保持传播轨迹和色散函数值方面具有独特的优势。     

A three‐crystal spectrometer for high‐energy resolution fluorescence‐detected X‐ray absorption spectroscopy and X‐ray emission spectroscopy at SSRF

A Johann‐type spectrometer for the study of high‐energy resolution fluorescence‐detected X‐ray absorption spectroscopy, X‐ray emission spectroscopy and resonant inelastic X‐ray scattering has been developed at BL14W1 X‐ray absorption fine structure spectroscopy beamline of Shanghai Synchrotron Radiation Facility. The spectrometer consists of three crystal analyzers mounted on a vertical motion stage. The instrument is scanned vertically and covers the Bragg angle range of 71.5–88°. The energy resolution of the spectrometer ranges from sub‐eV to a few eV. The spectrometer has a solid angle of about 1.87 × 0^?3 of 4π sr, and the overall photons acquired by the detector could be 10⁵ counts per second for the standard sample. The performances of the spectrometer are illustrated by the three experiments that are difficult to perform with the conventional absorption or emission spectroscopy. Copyright © 2016 John Wiley & Sons, Ltd.     

变折射率方形孔径平面微透镜阵列的聚焦和散焦特性

为提高变折射率平面微透镜阵列的填充率,利用光刻工艺和离子交换技术制备了填充率近达100%的方形孔径平面微透镜阵列,并对其透镜元及相邻透元间间隙构成的角落区域的成像进行了理论和实验研究.根据变折射率介质光线追迹法,利用MATLAB软件模拟,发现在透镜元区域和角落区域成像特性相反.成像系统测试表明:由于透镜元区域和角落区域的折射率分布变化规律不同,透镜元与角落区域对物体分别成倒立实像和正立虚像;透镜阵列可实现聚焦和散焦功能;角落区域得到充分的离子交换使得间隙足够小,形成了从该区域中心向外逐渐增大的新型梯度折射率模型.     

Design of fly's-eye lens for LCOS laser display

Design of optical system in laser display has always been an important research topic. From the aspect of decreasing the system volume and improving the light efficiency, it can be found that when the size of fly's-eye lens and the value of f/# are definite, the more fly's-eye arrays there are, the more useful it will be to the decrease of the optical engine size, which means that more honeycombs on fly's-eye lens and better dodging effect can be more beneficial for the decrease of the system size. After the optimal design for the rectangular elements on sub-fly's-eye lens and then doing 4000 ray tracing, the light transmittance turns out to be good with little parasitic light and scattering light.     

Specially profiled reflector for spherical front beams focusing

Focusing the power emitted from a source with spherical wave front by a specially profiled reflecting surface has been attempted using the simple ray tracing method. The reflector (mirror) surface profile that achieves such power redistribution is obtained from solving an ordinary first order differential equation using common numerical techniques. Furthermore, the proposed methodology can be useful to design complex reflectors for the electomagnatic and the acoustic systems, which finds broad engineering, industrial and biomedical applications.     

星载可见光相机成像仿真建模研究

针对星载可见光相机成像模拟在逼真度和灵活性方面的综合仿真应用需求,研究并提出了一种以三维场景为基础,以光线追踪技术为主要渲染核心,综合考虑卫星轨道和姿态、光照条件、物体光谱特性和周边环境、大气传输、遥感器成像性能等影响因素的全光路成像模拟技术的仿真模型.文中首先从完备性及可扩展性的角度尝试建立了成像仿真系统的综合模型框架,对整个成像链中的各个重要环节进行分层及模块化,并结合目前现有三维技术、光线追踪技术、传感器仿真技术的特点设计各模块之间的调用及接口关系,使其能在较好利用现有计算模型的同时能够对新的算法模型实现有效兼容.随后讨论了模型目前使用的镜头前辐亮度计算模块、光线路径计算模块和传感器效果仿真模块,并针对简单空间探测场景用C++编程语言实现了系统框架和关键模型,生成模拟图像,结果证明该模型在深空光照及大气效果方面有较好的表现,具备较高的仿真度和良好的适应性、扩展性,能够有效支撑卫星光学成像系统的指标论证、算法评估以及效能预估等应用.     

Methyl Pothoscandensate,a New ent‐18(4→3)‐Abeokaurane from Pothos scandens

Methyl pothoscandensate ( 1 ), a new molecular skeleton of ent‐18(4→3)‐abeokaurane, along with eight known compounds was isolated from the whole plant of Pothos scandens. The structure of the new compound was established by spectroscopic techniques and confirmed by single‐crystal X‐ray diffraction. The inhibitory activity of selected compounds against porcine respiratory and reproductive syndrome virus (PRRSV) was measured by the cytopathic effect (CPE) method. Compound 1 showed weak effect on PRRSV with an IC₅₀ value of 40.3±8.3 μM (TI=15.7).     

Novel Synthesis of 2‐Alkylquinolizinium‐1‐olates and Their 1,3‐Dipolar Cycloaddition Reactions with Acetylenes

Several 2‐alkylquinolizinium‐1‐olates 9 , i.e., heterobetaines, were prepared from ketone 11 , the latter being readily available either from pyridine‐2‐carbaldehyde via a Grignard reaction, followed by oxidation with MnO₂, or from 2‐picolinic acid (=pyridine‐2‐carboxylic acid) via the corresponding Weinreb amide and subsequent Grignard reaction. Mesoionic heterobetaines such as quinolizinium derivatives have the potential to undergo cycloaddition reactions with double and triple bonds, e.g., 1,3‐dipolar cycloadditions or Diels? Alder reactions. We here report on the scope and limitations of cycloaddition reactions of 2‐alkylquinolizinium‐1‐olates 9 with electron‐poor acetylene derivatives. As main products of the reaction, 5‐oxopyrrolo[2,1,5‐de]quinolizines (=‘[2.3.3]cyclazin‐5‐ones’) 19 were formed via a regioselective [2+3] cycloaddition, and cyclohexadienone derivatives, formed via a Diels? Alder reaction, were obtained as side products. The structures of 2‐benzylquinolizinium‐1‐olate ( 9a ) and two ‘[2.3.3]cyclazin‐5‐ones’ 19i and 19l were established by X‐ray crystallography.