半无界空间上函数的傅里叶-贝塞尔积分展开

柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间[0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.     

迭代卷积重建三维折射率场的计算机模拟

介绍了迭代卷积重建算法的教值过程，用ＴｕｒｂｏＣ．２．０开发了该算法的实用软件．通过计算机模拟运算，考查了其重建精度、重建误差与投影方向数和迭代次数的关系．结果表明，该软件对１８０°范围内均匀投影采样，投影数为６，迭代次数为８～１０次，仍具有较好的重建精度．     

光学层析技术中常见迭代重建算法的误差分析

为了得到较好的重建结果,对光学层析技术中常见迭代重建算法中的代数重建算法(ART)和同时迭代重建算法(SIRT)的重建参数进行分析,通过选择重建参数和计算机数值模拟达到重建要求.计算机数值模拟证明了松弛因子的选择对迭代重建算法的重建结果有非常重要的影响.在ART算法中,其他重建条件一定,松弛因子太大或太小时重建误差都会增大,松弛因子在0.4～1.5范围内时重建精度基本满足要求,最优松弛因子约为0.8;在SIRT算法中,松弛因子在4～12范围内时重建精度基本满足要求,最优松弛因子约为12.总结出代数重建算法和同时迭代重建算法不同条件下松弛因子选择的规律.在ART算法中,投影方向数增加松弛因子减小, 每方向投影数与重建分辨率对松弛因子无影响,松弛因子一定的情况下,投影数太小或太大误差会增大.在SIRT算法中,投影方向数增加松弛因子减小,并且投影方向数增加一倍最优松弛因子约减小为原来的50%; 每方向投影数增加最优松弛因子减小,且投影数增加一倍,最优松弛因子约减小原来的50%; 重建分辨率增加,最优松弛因子增加.     

基于高阶叠层矢量基函数的E-H时域有限元方法分析谐振腔和波导结构

将高阶叠层矢量基函数用于E-H时域有限元方法,电场和磁场用相同的基函数展开并同时求解,时间离散采用Crank-Nicolson差分格式使得时间步长的选取摆脱稳定性条件的限制,同时采用完美匹配层来截断计算区域.对三维谐振腔及波导结构进行数值模拟与分析,结果表明,相较于低阶基函数,高阶叠层矢量基函数可以有效提高E-H时域有限元方法的计算精度.     

Cosh-Hilbert变换反演的矩方法及其在单光子发射计算机断层成像中的应用

基于反演Hilbert变换的Tricomi公式和双曲余弦函数Taylor展开,给出一种反演双曲余弦Hilbert变换(CHT)的数值算法,并应用于单光子发射计算机断层成像.利用Taylor展开将函数的CHT变换表示为其Hilbert变换和由各阶矩组成的修正项.利用Tricomi公式得到一个关于函数各阶矩的线性方程组.通过对方程组的截断,可以求得函数的有限阶矩,并得到函数的近似重建.通过数值实验与精确重建公式进行比较,验证了算法的有效性.     

反射式超声计算机层析成像算法研究

本文通过数学推导证明,对于单发、单收反射式超声计算机层析成像,当声换能器离被成像物体较远时,可采用X-CT中的滤波-逆投影方法进行重建;当距离较近时,上述方法得到的重建像会大大失真。本文提出一种迭代修正方法,通过计算机模拟说明,与x-CT中常用的滤波-逆投影法相比,此方法可使重建像得到明显改善。     

基于多角度投影激光吸收光谱技术的两段式速度分布流场测试方法

针对具有明显速度梯度的非均匀流场速度分布在线测试难题,提出了基于多角度投影的激光吸收光谱多普勒速度分布测试方法,利用多角度投影吸收光谱信息低频能量相对变化对两段式速度分布区间长度与对应速度值进行耦合求解.建立不同投影角度下吸收光谱平均频偏值与不同速度区间频偏差值之间的函数关系,提出了基于傅里叶变换的光谱信号低频能量变化分析方法,解决了不同速度梯度条件下光谱信号微弱变化检测难题.采用7185.6 cm~(–1)波段H_2O特征谱线结合三条投影光路实现了对于两段式速度分布模型的快速重建,研究了投影角度以及不同幅值噪音对速度分布计算的影响.分析表明该方法对于具有明显速度梯度的流场中高速区速度值重建结果最佳,相对误差0.9%,同时测量噪音对高速区速度值重建结果影响最小.投影角度增大有利于增强重建方程中不同速度区间光谱频偏差值对速度区间长度比值的灵敏度,提高测量精度.考虑到系统测量空间分辨率限制, 0°, 30°, 60°是较为理想的光路分布角度.研究结果对于推动激光吸收光谱技术在发动机诊断及气体动力学研究中的应用具有重要意义.     

高阶间断伽辽金时域有限元方法分析三维谐振腔

从一阶麦克斯韦旋度方程出发,研究一种区域分解时域有限元目的——高阶间断伽辽金时域有限元目的.其中对时间的离散采用Crank-Nicolson差分格式,电场和磁场采用相同阶数的高阶矢量基函数展开.分析三维谐振腔问题,数值结果表明,目的 中时间步长的选取可以摆脱CFL稳定性条件的限制;此外,与基于常用Whitney矢量基函数的目的 相比,采用高阶矢量基函数可以明显地提高计算精度及计算效率.     

信息光学 光学信息处理、图像识别

O4382006010288基于哈特曼波前探测层析重建三维温度场=Tomographicreconstruction of3-Dtemperature field based on Hart mannwavefront sensing[刊,中]/戴云(中科院光电所.四川,成都(610209)),张雨东…∥中国激光.—2005,32(10).—1406-1410基于哈特曼波前探测的流场层析测量技术结合了光学波前探测技术和计算机层析重建技术。系统由哈特曼传感器探测平行光束穿过流场后的投影波前,提取流场在多方向上的投影数据,采用计算机层析技术重建流场物理量的空间分布。为了验证系统的可行性和标定系统重建精度,对静态圆对称折射率场进行层析重…     

基于多波长激光吸收光谱技术的气体浓度与温度二维分布遗传模拟退火重建研究

利用可调谐半导体激光吸收光谱技术实现气体浓度温度二维分布重建.设计了气体浓度温度二维分布重建测量系统,采用四路波分复用技术以减少投影光路布置数量和增加气体吸收测量信息.针对于图像重建过程中建立的非线性投影方程组,将遗传算法与模拟退火算法相结合进行求解,在实现全局最优搜索基础上提高算法搜索效率.建立燃烧环境下H2O浓度温度二维分布模型,借助于近红外波段1.3—1.5μm范围内4条H2O气体吸收谱线,利用数值模拟计算方法进行了气体分布重建,重建结果与模型符合得很好.通过在投影数据中添加不同比例的随机误差,考察其对气体分布重建结果的影响.研究表明,气体浓度分布重建结果对于投影误差不敏感,而增加投影误差幅值将导致温度分布重建均方误差增大。     

Spectral radial basis functions for full sphere computations

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged.     

Spectral radial basis functions for full sphere computations

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged.     

Dual Principles in Maximum Entropy Reconstruction of the Wave Distribution Function

Maximum entropy methods are used for reconstructing the distribution of energy in wave vector space from frequency spectra observed on board satellites. The reconstruction scheme is based on a modified entropy function, and dual principles are used to solve the resulting optimization problem. Our scheme is not limited to reconstructions of wave distribution functions, but it should be useful also for solving other types of underdetermined inverse problems.     

Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s and not so for orders between 2-s and 1, where s, 1相似文献   

量子力学可视化的计算机辅助表述——电子云、壳层结构以及共价键的三维重构

文章简要说明如何应用计算机三维重构技术 ,以MATLAB为开发工具研制成一个量子力学可视化的教学软件包中的一个重要组成部分———氢原子和多电子系统电子云、壳层结构和分子共价键的三维重构 .软件中所有形象表述都以量子力学的严格理论计算为基础 ,并且注意到量子力学不同寻常的基本概念的贯彻 .它们涉及到了单电子和多电子系统波函数的计算及其近似处理、密度矩阵的概念、斯莱特 (Slater)行列式等比较深入的数学物理问题     

Local Constraints Satisfied by Realizable Correlation Functions

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new, local constraints—each a consequence of the reciprocal-space non-negativity constraint—that are satisfied by the differentiable correlation functions.     

声辐射模态和球谐波函数在球源声场重建中的比较

声辐射模态和球谐波函数在球源声场重建中均有应用,两者具有很多相似性,都具有相同的多极子辐射模式和"群组"分布特性。有观点认为球形声源的声辐射模态向量即为球谐波函数,但两者的内在关系一直缺乏有效的证明。为分析两种基函数的相似性及在球源声场重建领域的差异,在理论上建立了两者的内在联系,在应用上比较研究了基于两种基函数的声场重建方法的有效性和可靠性。数值算例结果表明,在中高频段时基于两种函数的声场重建效果相当,但在低频段尤其是存在干扰源的非自由场条件下的声场重建应用中,基于声辐射模态的声场重建方法能得到更高的重建精度。可见,声辐射模态具有较为明显的声场重建优越性,这为利用声辐射模态和球谐波函数进行球源声场重建提供了理论参考。      

Regularity of the density of states in the Anderson model on a strip for potentials with singular continuous distributions

We derive regularity properties for the density of states in the Anderson model on a one-dimensional strip for potentials with singular continuous distributions. For example, if the characteristic function is infinitely differentiable with bounded derivatives and together with all its derivatives goes to zero at infinity, we show that the density of states is infinitely differentiable.     

势问题的径向基函数——局部边界积分方程方法

将基于径向基函数构造的具有插值特性的近似函数和局部边界积分方程方法相结合，建立了求解势问题的径向基函数——局部边界积分方程方法，推导了相应离散方程.与其他边界积分方程的无网格方法相比，本文方法具有数值实现过程简单、计算量小、精度高的优点，并可直接施加边界条件.最后通过算例说明了该方法的有效性. 关键词： 径向基函数 无网格方法 局部边界积分方程 势问题     

A new differential calculus on a complex banach space with application to variational problems of quantum theory

It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banach spaces. It is shown that this result makes the calculus largely inapplicable to the solution of variational problems of quantum mechanics. A new concept of differentiability called semi-differentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-valued functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (1969) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus on banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear functions as particular cases.