矢量场的散度在运动空间区域中的体积分随时间变化率的严密理论

给出运动空间区域中充满介质的情况下,以及运动空间区域中包含有介质和真空的情况下,矢量场的散度在运动空间区域中的体积分随时间变化率的两种计算方法.阐明了若以一种特别的方法来看待空间积分区域的变动,那么两种情况就可以用统一的方式来计算.指出在运动空间区域中包含有介质和真空的情况下,如果保留速度v在积分区域V的边界面S上的值和实际情况一样,而赋予区域V以一个其空间变化率连续或者分块连续的新的速度场v(r,t),那么锁定体元的计算方法仍然适用.     

远轴高斯波的矢量场理论

提出了描述远轴高斯光波的矢量场方法,推导了精确的远场传播公式,讨论了矢量场远轴高斯波的远场光波特征和传播规律,并与标量场理论作了比较,指出了标量场理论的适用范围． 关键词：     

赏析矢量场的场管及通量问题

物理学中常把某个物理量的时空分布叫做场,场是物质存在的重要形式.矢量场即是常见的的一类场,所谓矢量场,就是在空间各点存在着的一个矢量,其大小和方向是空间位置及时间的函数.对一个不随时间变化的矢量场,矢量的大小和方向是空间位置的函数.如果矢量A(黑斜体字母表示矢     

色噪声驱动的双奇异随机系统随时间演化的熵变化率上界

通过变换的方法讨论了一类高斯色噪声驱动的双奇异随机系统所对应的Fokker-Planck方程, 并结合Shannon信息熵的定义及Schwartz不等式原理给出了经变换后该系统随时间演化的熵变化率上界的精确表达式. 分析了奇异性强度参数、噪声相关时间与耗散参数对熵变化率上界的显著影响.     

非傍轴矢量高斯光束单缝衍射的严格理论

提出非傍轴矢量光束衍射严格的电磁场理论,并以非傍轴矢量高斯光束的单缝衍射为例加以说明.与基于矢量瑞利-索末菲衍射积分推出的解析结果做了数值计算比较,表明了二者的一致性.对理论的进一步推广做了简要讨论. 关键词： 严格的电磁场衍射理论 矢量瑞利-索末菲衍射积分 非傍轴矢量高斯光束的单缝衍射     

计算动态系统网格通量场的驿站重要抽样方法

对与时间有关输运问题计算条件下,全系统不同网格体通量计算统计涨落较大,甚至个别网格很难得到计数的现象,提出驿站重要抽样方法.研究可以选择的重要性函数,给出抽样方法,推导重要性偏倚抽样的源粒子纠偏权重公式.经过推导证明连续多时间步抽样计算不存在粒子纠偏权发散问题.数值模拟结果表明,采用驿站重要抽样方法,全系统精细网格通量场计算精度基本一致,整体计算结果得到明显改善.     

非傍轴矢量高斯光束的光强表示

 基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。     

非傍轴矢量高斯光束的光强表示

基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。     

关于带电粒子在磁单极场中运动的一些评注

指出教科书中关于带电粒子在磁单极场中的散射与电荷量子化的简化讨论存在明显的错误.通过对运动轨迹的仔细分析,得出的物理图像是:粒子从入射到出射,极距角θ和方位角?均发生了变化.特别是,当瞄准距离很大时,?的变化近似为±π/2.计算了角动量的变化并得到了合理的结果.顺便讨论了散射截面的计算.     

非傍轴矢量余弦-高斯光束两种光强表示的比较研究

从矢量瑞利-索末菲衍射积分公式出发,以非傍轴矢量余弦－高斯(CoG)光束为例,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了比较研究.对非傍轴矢量CoG光束轴上和横向光强分布详细的数值计算和比较结果表明,两种光强表示式之间的相对误差η与w0/λ、z/λ和偏心参量b有关,其中w0,λ和z分别为束腰宽度,波长和传输距离.当偏心参量b较小,且束腰宽度与波长相比不很小时,例如,b≤0.8,w0/λ≥0.8,z/λ=10时,二者间的最大相对误差ηmax＜2%,传统光强公式可以使用.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

A characterization of strict Jacobi-Nijenhuis manifolds through the theory of Lie algebroids

We obtain a characterization of strict Jacobi-Nijenhuis structures using the equivalent notions of generalized Lie bialgebroid and Jacobi bialgebroid.     

Structural polarization properties of vector Gaussian beam in the far field

Based on the vector angular spectrum representation of optical beam and the method of stationary phase, the analytical TE and TM terms of vector Gaussian beam have been presented in the far field. By using the local polarization matrix, the polarization properties of the TE and TM terms in the far field are investigated, and it is found that the degree of their polarization is only determined by the spatial location. When the source is completely polarized, the TE and TM terms are both completely polarized in the far field. When the source is completely unpolarized, the TE and TM terms in the far field are partially polarized. The whole beam is also partially polarized except on the propagating axis. Moreover, the degrees of polarization of TE and TM terms are both larger than that of the whole beam.[第一段]     

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.     

Analytical structure of an apertured vector Gaussian beam in the far field

Based on the angular spectrum representation of the Maxwell’s equations and the complex Gaussian expansion of the aperture function, the structure of an apertured vector Gaussian beam in the far field is presented in the integral form. By means of the method of stationary phase, the analytical vectorial structures are obtained. According to the analytical expressions, the characteristics of vectorial structure of an apertured Gaussian beam are investigated in the far field. The influence of a linearly polarized angle on the vectorial structure is also studied in the far field. This research provides a novel approach to further comprehend the vectorial property of an apertured Gaussian beam.     

Analytical vectorial structure of non-paraxial nonsymmetrical vector Gaussian beam in the far field

Based on the vectorial structure of non-paraxial electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of non-paraxial nonsymmetrical vector Gaussian beam in the far field are presented. According to the analytical electromagnetic fields of the TE and TM terms, the energy flux distributions of the whole beam, its TE and TM terms are investigated. Moreover, the influences of non-symmetries on the energy flux distributions of the whole beam, its TE and TM terms are also analyzed, respectively. This research reveals the internal vectorial structure of non-paraxial laser beam in the far field and is useful to the propagation of non-paraxial laser beam.     

Stability of capillary waves with arbitrary symmetry on the surface of a jet in a longitudinal electric field periodically varying with time

The Mathieu differential equation for the evolution of the amplitudes of arbitrarily symmetric capillary waves (with arbitrary azimuthal numbers) propagating over the surface of a incompressible dielectric cylindrical liquid jet is analyzed. The jet is placed in a time-periodic uniform electric field that is parallel to the symmetry axis of the jet unperturbed by the wave flow. It is found that the time-varying electric field pressure parametrically builds up both axisymmetric waves on the jet surface, flexural waves, and flexural deformation waves. At a fixed frequency of the external field, waves with different wavelengths and symmetries (different azimuthal numbers) may build up simultaneously in the main demultiplication resonance, as well as in secondary and tertiary resonances. The parametric buildup of flexural deformation waves has a threshold relative to the external field frequency: it takes place at the field frequency exceeding a certain value depending on the jet radius and physicochemical properties of the liquid.     

The role of the frozen surface approximation in small wave-height perturbation theory for moving surfaces

In the standard development of the small wave-height approximation (SWHA) perturbation theory for scattering from moving rough surfaces [e.g., E. Y. Harper and F. M . Labianca, J. Acoust. Soc. Am. 58, 349-364 (1975) and F. M. Labianca and E. Y. Harper, J. Acoust. Soc. Am. 62, 1144-1157 (1977)] the necessity for any sort of frozen surface approximation is avoided by the replacement of the rough boundary by a flat (and static) boundary. In this paper, this seemingly fortuitous byproduct of the small wave-height approximation is examined and found to fail to fully agree with an analysis based on the kinematics of the problem. Specifically, the first order correction term from the standard perturbation approach predicts a scattered amplitude that depends of the source wave number, whereas the kinematics point to a scattered amplitude that depends on the scattered wave number. It is shown that a perturbation approach in which an explicit frozen surface approximation is made before the SWHA is invoked predicts (first order) scattered amplitudes that are in agreement with the analysis based on the kinematics.