A symmetric integrated radial basis function method for solving differential equations

In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.     

Coincidence Imaging and interference with coherent Gaussian beams

we present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between quantum entangled photon pairs and coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation a quantum nature. Selected from Acta Sinica Quantum Optica, 2005, 11(4)(in Chinese)     

对于金融资产波动率估计的双域组合方法

Time- and state-domain methods are two common approaches for nonparametrically estimating the volatility of financial assets. Economic conditions vary over time in real financial market. It is reasonable to expect that volatility depends on both time and price level for a given state variable. Recently, Fan, et al （2007） proposed the idea of dynamically integrated method in both time-and state domain. This idea has become an interesting topic in the estimation of volatility. In this paper, our purpose is to discuss the integrated method in the estimation of volatility. Simulations are conducted to demonstrate that the newly integrated method outperforms some old ones, and the results of simulations demonstrate this fact. Furthermore, we establish its asymptotic properties.     

Transformation optics and cloaking

Invisibility, a long sought-for speculation in science fiction, has been turned into reality in the laboratory through the use of a theoretical technique called Transformation Optics. The principles of transformation optics show that any desired smooth deformation of the electromagnetic field can be implemented exactly by an appropriately engineered metamaterial. All demonstrations of cloaking to date have had limitations, however, reflecting our technological inability to implement the transformation optics algorithm exactly. However, the scientific principles leading to perfect invisibility are now established, and practical improvements on the initial designs are now occurring very rapidly. Most recently, researchers have re-examined transformation optics to include time as well as space, describing and then implementing the concept of a cloak that hides events, a conceptual breakout that promises many new applications. This review describes the general ideas underlying transformation optics, and how the various types of cloak based on these ideas have been implemented practically to date.     

利用法拉第效应进行永磁体磁场二维光学成像

借助于法拉第磁致旋光效应,以ZF6玻璃为磁旋光介质,设计了适当的光学系统,对永磁体磁极附近磁场的分布进行了光学二维成像.利用自编的图像采集软件采集了一系列原始图片,并利用自编的图像处理软件对这些原始图片进行了处理,完成了检偏过程.分别得到了透射成像方式和反射成像方式下永磁体磁场的分布图像,这些图像正确反映了永磁体磁场的实际分布.本研究工作为宏观尺度磁场的观测与测量提供了一种有效的手段.     

不同光照强度和光质对铁线莲品种繁星(Clematis‘nelly moser’)不定芽诱导和生长的影响

以铁线莲品种繁星(Clematis' nelly moser’)的带节茎段为材料,研究不同光照强度和光质对铁线莲不定芽繁殖的影响.以MS为基本培养基(含有0.2 mg/L 1-萘乙酸和2 mg/L 6-苄氨基腺嘌呤),设置光照强度梯度为0、500、2 000、3 000和4 000 Lux的白光光照;用透明玻璃纸得到蓝(440 nm)、绿(560 nm)、红(650 nm)3种光质,以白光为对照组,强度均为3 000 Lux.结果表明:在光照强度为3 000 Lux的白光光照下,不定芽的诱导效果最好,其诱导频率和每个外植体上不定芽的数量分别为100％和4.4,每个外植体上不定芽的平均高度为5.66cm,平均节数为4.6个;蓝光能够显著提高不定芽的诱导数量,是相同光强白光诱导数量的1.27倍,蓝光下不定芽SOD和CAT的最大值显著高于其它光质下的数值,且叶绿素a和b的比值最大.     

与Glauber-Lachs态相互作用的双原子间的纠缠演化

利用全量子理论,对伴随多光子跃迁时与Glauber-Lachs态相互作用的两个原子间的纠缠特性进行了研究,主要讨论了相干平均光子数、热平均光子数和跃迁光子数对系统中原子间的纠缠特性的影响.结果表明:系统中原子间的纠缠度是相干平均光子数的非单调函数;随着热平均光子数和跃迁光子数的增加,系统中原子间的纠缠度有减小的趋势,伴随双光子跃迁时系统中原子间的纠缠度随时间的演化呈现周期性.     

拉曼效应对负折射介质中超短脉冲传输的影响

通过数值法对包含拉曼延迟响应的(3+1)维非线性薛定谔方程进行求解,研究了超短脉冲激光在负折射介质中传输时拉曼效应对自聚焦传输特性的影响,着重分析其不同与常规介质的反常传输现象.结果表明:由于负的折射率影响,拉曼效应将导致超短脉冲在自聚焦过程中频谱发生蓝移现象,这与常规介质对应情形相反;而它对负折射介质中超短脉冲的自聚焦特性的影响与常规介质相同,即拉曼效应将诱导自聚焦效应首先发生在脉冲的前沿.本文研究工作对将来利用负折射介质来操控超短光脉冲串产生、自聚焦等许多实际应用领域研究具有重要的指导意义.     

湍流中漫射目标偏振部分相干激光的闪烁特性

采用广义惠更斯-菲涅耳原理和矩阵光学理论,研究了湍流大气中偏振部分相干激光波束从发射机到目标和从目标到接收机双程路径的闪烁特性。将产生任意偏振光束的琼斯矩阵和ABCD传输矩阵进行结合,围绕接收机处波场四阶矩展开推导,得出双程路径下偏振部分相干激光波束在接收机处的闪烁指数表达式,数值分析了大气折射率结构常数、激光波束的波长、束宽、相干长度对接收机处光强闪烁指数的影响。结果表明:偏振部分相干激光波束的闪烁指数随着目标与发射机之间距离呈现先增大、到达峰值后逐渐减小的变化趋势;相干性差的光束产生的闪烁指数小,相干长度微小的变化将会产生较大的闪烁指数变化,相干性好的光束产生较大的闪烁指数,但是相干长度的变化对闪烁指数的影响很小。     

空调焓差试验装置的检测方法

随着我国对空调能效检测要求的不断提升,空调焓差试验装置得到越来越广泛的使用。以空调焓差试验装置的发展和现状、国内外检测依据入手,对其检测方法进行研究。同时通过对系统分析,探讨其检测方法,为我国空调企业及检测实验室提供参考。