Influence of various degradation conditions on the properties of gas-generating soils in the process of their decontamination

The properties of gas-generating soils (GGS) in the process of biofermentation under anaerobic and aerobic conditions are studied. The degradation of organic matter (OM) in a soil under natural occurrence conditions (without free access of air oxygen) at temperatures from 10 to 12°C is demonstrated to proceed at a specific reaction rate of k = 0.096 year^?1. The main phase of gas generation (biogas formation) is shown to take 15 years, with the content of methane in the biogas being 60?80 vol %. It has been established that, under the conditions of forced aeration of the GGS array, the specific reaction rate of OM degradation increases 10-fold, to 0.9673 year^?1, with a nearly complete decomposition of OM taking 1.5?2.0 years. A prerequisite for achieving of the predicted result is the maintenance of the environment humidity at a level not lower than 50%. Application of an alternative method, a thermal treatment of GGS increases the degree of OM decomposition to 59% within 4 h at 200°C and to 75% within 2 h at 300°C. In this case, residual organic substances are carbonized in the course of thermal treatment, transforming into a material resistant to microbiological decomposition. In fact, after heating at 200?300°C, GGS becomes inert from the gas-geochemical point of view.     

平面波经小圆孔非傍轴衍射的轴上光强解析分析

用亥姆霍兹 基尔霍夫积分定理和基尔霍夫边界条件,推导出了平面波经小圆孔非傍轴衍射时轴上强度的简单解析表达式,研究了平面波经小圆孔后整个衍射空间非傍轴的轴上光强分布.给出了计算圆孔菲涅尔数的精确公式,重新检查了通常的菲涅尔数公式的有效性.数值计算显示,应用解析表达式所得的结果与应用衍射积分公式所得的结果完全一致.     

狭缝式裂变探测系统的中子灵敏度解析计算方法

 利用基于解析公式的理论方法来计算狭缝式裂变探测系统的中子灵敏度。采用积分和泰勒展开法推导了铀裂变材料在中子作用下产生的碎片数目及PIN探测器接收碎片的概率,并得到该系统的中子灵敏度理论计算公式。在D-T中子源上对该探测系统的中子灵敏度进行了实验标定,并将实验结果与解析公式计算得到的理论值进行比较。结果表明：理论计算值与实验结果保持一致,两者之间的偏差小于10%。     

三维静电场线性插值边界元中的解析积分方法

提出求解三维静电场的三角形线性插值边界元解析积分方法.针对含1/R和1/R²的积分项,将单元形状函数分解为常数项、含x的线性项和含y的线性项,从而将边界单元积分简化为6个基本积分组合,并导出其解析计算公式,避免了因形状函数改变而导致的重复计算.该方法不仅可以准确计算远离奇异情况下的边界元积分,而且可以准确计算一阶和二阶接近奇异积分以及一阶奇异积分.计算结果表明,在接近奇异积分和奇异积分比较突出的问题中,当数值积分方法不能给出正确结果时,用同样的边界元网格,解析积分方法可以给出正确的结果,提高了三维静电场线性插值边界元法的计算精度.     

On the solution of the kinetic equation for a heat flux between concentric spheres

The problem of calculating a heat flux in a spherical layer is considered. The results are obtained in terms of the Bhatnagar-Gross-Krook model and the Boltzmann collision integral. A general (independent of the form of the kinetic equation and the solution method) expression for the heat flux as a function of the energy accommodation coefficient is derived. The results are compared with the experiment and the analytical results obtained previously.     

用级数拟合求圆电流磁场解析解

采用将圆电流磁矢势表达式中一部分展成分数，使被积函数变成可积分的函数，用解析函数拟合积分的级数，代替无穷级数求和运算，得到可以计算圆电流在空间任保一点磁场的解析解，解决了计算非近轴区圆电流磁场问题。     

Analysis of the evolution of perturbations in a magnetized collisionless plasma with an integral-equation technique

Summary A technique recently proposed to study the classical problem of the evolution of small perturbations in a collisionless unmagnetized plasma is extended to a magnetized plasma. A time-convolutive integral equation for the plasma density is obtained from the Vlasov equation for a homogeneous plasma in a uniform, stationary magnetic field. The equation can be solved by means of simple numerical algorithms and, in some cases, analytical solutions can be obtained. The procedure proves to be analytically simpler than the classical one and is more convenient from a numerical point of view. Techniques of solution are presented and analytical and numerical results for electrostatic perturbations are discussed.     

表面电荷法平面元电荷系数的半解析解法

针对在线性及高次电荷估计下,表面电荷法中全解析法对平面元电荷系数求解和实现较复杂的问题,提出一种半解析法.将系数积分由局部坐标系变换到整体坐标系下分离参数的二重积分,利用内层积分存在解析解的特点,将二维问题降为一维,方便数值积分计算.对于对数奇异积分问题采用辅助函数法消除.通过算例与全解析法计算精度进行比较,结果表明,在一定的单元划分下,可达到很高精度,具有一定可行性.     

Molecular Integral for the Double Electron-Repulsion Potential： A Closed Form Underived for Forty Years

A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

Horizontal-Longitudinal Spatial Correlation of Acoustic Field with Deep Receiver in the Direct Zone in Deep Water

The horizontal-longitudinal correlation of acoustic field for the receiver near the bottom is analyzed by using numerical modeling. An approximate analytical solution of horizontal-longitudinal correlation coefficient is derived based on the ray method. Combining the characteristic of Lloyd's mirror interference pattern, the variability of acoustic field and its effect on horizontal-longitudinal spatial correlation are discussed. The theoretical prediction agrees well with the numerical results. Experimental results confirm the validity of analytical solution.Finally, the applicability of the analytical solution is summarized. The conclusion is beneficial for the design of bottom-moored array and the estimation of integral time for moving source localization.     

Recurrence propagation equation of Hermite-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples.     

Analytical expressions for the correlation function of a hard sphere dimer fluid

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.     

Charm quark energy loss in QCD matter

The energy loss of heavy quarks in a quark-gluon plasma of finite size is studied within the light-cone path integral approach. A simple analytical formulation of the radiative energy loss of heavy quarks is derived. This provides a convenient way to quantitatively estimate the quark energy loss. Our results show that if the energy of a heavy quark is much larger than its mass, the radiative energy loss approaches the radiative energy loss of light quarks.     

Wigner distribution function of Gaussian beam through an apertured and misaligned ABCD optical system

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical expressions of Wigner distribution function for fundamental mode Gaussian beam through an apertured and misaligned ABCD optical system are derived. Compared with the aligned case, results show that the misaligned optical system will introduce in the output Wigner distribution function a coordinate shift in space-frequency plane. To examine the analytical results, some numerical simulations are carried out and the absolute errors between analytical results and numerical integral ones are presented. It is shown that the approximate analytical results are proper and ascendant.     

Propagation characteristics of linearly polarized Bessel-Gaussian beams through an annular apertured paraxial ABCD optical system

By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture.     

流管实验装置中声传播计算的模态方法

流管实验装置是测量有流动情况下航空发动机消声短舱内声衬声阻抗的主要装置。本文发展了一种解析的模态匹配方法进行在平均流有声衬条件下矩形流管中声传播的计算。用同伦方法求解特征值问题,并与用环绕积分求解的结果进行比较。声场通过轴向阻抗间断面的声压和声质点速度积分相等计算。第一个算例是无流动、硬壁、有限长、考虑端口反射的情况,并与北航流管实验台测量数据进行了对比;第二个算例为有流动情况下有限长声衬管道不考虑端口反射的声场计算,它与文献中NASA流管实验结果和CAA计算结果符合得很好。     

基于Burton-Miller方程的轴对称结构声学边界元方法

提出了一种求取轴对称结构任意边界条件下声辐射特性的边界元方法。采用Burton和Miller改进型公式将高阶奇异项转化为弱奇异项之和,保证声辐射参数的唯一性,且计算简单精确。将结构表面声压与振速按照旋转轴角度进行Fourier级数展开,利用级数的正交性建立各项待定系数的求解公式;然后转化格林函数的法向偏导为切向偏导,方便直接计算各项积分,并将面积分公式表示为沿结构边界的线积分和沿旋转角度的积分;进一步采用二次等参单元离散结构边界线,建立声压与振速的关系矩阵,从而确定结构声辐射参数。以脉动球源和横向振动球源为例计算,与解析解和传统边界元法结果作对比,说明该方法的有效精确性。     

Transmission of reverberant sound through orthotropic,viscoelastic multilayered plates

In previous work the authors have studied acoustic transmission through orthotropic multilayered plates under oblique plane wave excitation. In this paper an extension of this work to the case of reverberant sound excitation is reported. In order to compute the mean transmission loss over the wave incidence angles an analytical method has been adopted, rather than the classical double integral calculation which is very cumbersome. The influences of layering, damping, and orthotropy are discussed. A comparison between theoretical and experimental results is presented.