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1.
从辐射传输方程中相函数的展开方法出发,分别介绍了δ-M展开法和δ-fit展开法,并对这两种相函数展开方法进行了比较。结果表明,在相函数展开中,当所取勒让德多项式的阶数相同时,δ-M法的图像始终在真实相函数附近波动,始终无法逼近真实的相函数的值,而δ-fit法符合较好。  相似文献   

2.
推广的Painlevé展开及KdV方程的非标准截断解   总被引:8,自引:0,他引:8       下载免费PDF全文
利用奇性流形的任意性,选用不同的展开函数及非标准截断展开于KdV方程,得到了许多用复杂隐函数表示的精确解  相似文献   

3.
少数投影局部基函数展开层析重建   总被引:2,自引:1,他引:1  
戴云  张雨东  李恩德  杨泽平 《光子学报》2005,34(11):1719-1723
对6种常见的基函数展开通过计算机仿真分析、比较其重建效能.结果表明,对于少数投影计算机层析重建,采用连续可导的局部基函数展开比采用非连续可导的脉冲基函数展开具有更高的重建精度.而对于各种连续可导的基函数,其重建精度大致相当,基函数的选取应重点考虑其投影矩阵计算的难易程度.  相似文献   

4.
利用高阶窗函数结合连分式展开等技术研究并建立一种水平层状各向异性介质中电磁场并矢Green函数的快速有效算法. 首先借助于高阶窗函数将构成并矢Green函数的Sommerfeld积分转化成广义快速下降路径上积分,并给出高阶窗函数Hankel变换的一种新的更高阶幂级数展开式以及严格的Lommel函数表达式,以满足在全空间上高精度计算并矢Green函数的要求. 在此基础上,用Bessel函数的零点将积分路径划分成一系列小区间并通过改进的自适应Gauss求积公式确定各个小区间上的积分值,然后引入连分式展开法对各个区间上的积分值求和,从而使整个积分的收敛效率得到大大提高. 最后通过数值结果验证本方法的有效性. 关键词: 高阶窗函数 连分式展开 并矢Green函数 层状各向异性介质  相似文献   

5.
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.  相似文献   

6.
本文发展了使用幂次式展开收敛域中含有支点的复变函数的方法.在无穷阶支点下,函数的展开式化为积分的形式,称之为洛朗变换.文章还探讨了部分典型函数的展开结果及其完备性问题,并提出了使用连续复幂次代替实幂的方法.最后,举出一例简释了该方法在信号系统中的实际应用,展望了应用前景.  相似文献   

7.
冰晶粒子散射相函数的多项式展开可以应用于卷云条件下大气辐射传输模式的计算。本文利用广义球函数对表面严重粗糙的冰晶粒子相函数进行展开,并对表面严重粗糙的实心棱柱模型、实心棱柱聚合物模型和一般种类混合模型3种冰晶粒子的展开系数特性进行分析研究,数值计算结果表明了广义球函数对表面严重粗糙的冰晶粒子多项式展开的有效性。  相似文献   

8.
程平东 《计算物理》2001,18(5):451-456
比较了节块展开法(NEM),节块格林函数法(NGFM)和节块傅立叶展开法(NFEM)的偏中子通量展开技术,证明了NFEM的精度高于任何有限阶NEM,而与NGFM相当。  相似文献   

9.
椭圆孔光子晶体光纤的本地正交函数模型   总被引:5,自引:1,他引:4       下载免费PDF全文
提出了一种用于分析椭圆孔光子晶体光纤的正交函数模型.发展了一种新型超格子的构造方法,将光子晶体光纤的横向介电常数表示为两种周期性结构叠加,这两种周期性结构分别用余弦函数展开;同时将横向电场以Hermite-Gaussian函数展开.利用正交函数的性质,将全矢量波动方程转化为矩阵本征值问题,求得两偏振模式传输常数.利用此模型可以研究圆孔及椭圆孔光子晶体光纤的模式特性、色散特性、偏振特性等. 关键词: 光子晶体光纤 超格子 正交函数 本征值问题  相似文献   

10.
Lam函数和非线性演化方程的多级准确解的不变性   总被引:4,自引:0,他引:4       下载免费PDF全文
刘式适  陈华  付遵涛  刘式达 《物理学报》2003,52(8):1842-1847
利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.并在Lam方程和Lam函数的基础上,应用 Jacobi椭圆函数展开法求出了非线性演化方程的多级准确解,从而得到了多级准确解中存在的守恒形式. 关键词: Lam函数 Jacobi椭圆函数 多级准确解 非线性演化方程 扰动方法 不变性  相似文献   

11.
We develop the theory of operators defined on a space of holomorphic functions. First, we characterize such operators by a suitable space of holomorphic functions. Next, we show that every operator is a limit of a sequence of convolution and multiplication operators. Finally, we define the exponential of an operator which permits us to solve some quantum stochastic differential equations.  相似文献   

12.
In the paper we examine some properties of the generalized coherent states of the Barut-Girardello kind. These states are defined as eigenstates of a generalized lowering operator and they are strongly dependent on the structure constants. Besides the pure coherent states we focused our attention on the mixed states one, which are characterized by different probability distributions. As some examples we consider the thermal canonical distribution and the Poisson distribution functions. We calculate for these cases the Husimi’s Q and quasi-probability P-distribution functions.  相似文献   

13.
Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions.  相似文献   

14.
Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions.  相似文献   

15.
(2+1)维Boussinesq方程的Backlund变换与精确解   总被引:4,自引:0,他引:4       下载免费PDF全文
曾昕  张鸿庆 《物理学报》2005,54(4):1476-1480
借助于符号计算软件Maple,对方程的种子解作适当的未知函数替换,然后利用Backlund 变 换通过具体的符号演算获得了(2+1)维Boussinesq方程的一系列精确解.这些解包括类孤子解 和有理解,其中有的解中含有任意函数,当任意函数取特殊函数时,这些解具有丰富的结构 ,有些结构可能对物理现象的研究是有意义的. 关键词: (2+1)维Boussinesq方程 Backlund 变换 精确解 类孤子解  相似文献   

16.
New exact solutions to some difference differential equations   总被引:6,自引:0,他引:6       下载免费PDF全文
王振  张鸿庆 《中国物理》2006,15(10):2210-2215
In this paper, we use our method to solve the extended Lotka--Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of \sinh and \cosh, periodic solutions presented by trigonometric functions of \sin and \cos, and rational solutions. This method can be used to solve some other nonlinear difference--differential equations.  相似文献   

17.
We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.  相似文献   

18.
利用数值计算的方法求解了一维理想双势阱模型的基态及低激发态能级和相应的波函数,将双势阱之间的间距、双势阱的相对深度和双势阱的宽窄与实际的物理问题建立了联系,并分析了它们对一维双势阱的能级和相应波函数的影响,定性地模拟了双原子分子和原子中的双势阱问题.  相似文献   

19.
We summarize and deepen existing results on systems of orthogonal pure states in the context of Jordan–Banach (JB) algebras and C* algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposing points by continuous functions, separating sets by continuous functions, and multiplicativity of pure states.  相似文献   

20.
Spectral reflectance is a significant physical property of materials. It plays an important role in color constancy, illumination modeling, and color reproduction. Spectral reflectance basis functions are the most important impact factors for spectral reflectance recovery. Previous methods mainly calculated basis functions for the reflectance spectra data sets by employing the principle component analysis (PCA) and its improved methods. In this paper, we present a new method to solve this problem. Specifically, we propose a new cost function and some constraint conditions to convert the problem into an optimization problem by minimizing the cost function. Unlike the PCA method which yields the orthogonal basis functions for approximating the reflectance spectra, our method yields the nonorthogonal basis functions for better approximating the reflectance spectra. Experimental results show that our derived basis functions are better than those obtained by the PCA method for reflectance spectra recovery.  相似文献   

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