关於中子在两种介质中的慢化问题

本文根据年龄理论,考虑下列问题:二介质由球面r=a分开,球面外的介质一直延伸到无限,球面内的介质中在r=R处放有壳形单能快中子源;要求二介质中由此引起的中子慢化密度的空间分布。求解时应用了拉氏变换的方法。求出了适用於(τ₁)^1/2≤α情形的展开式,这里τ₁是中子在球面内介质中的年龄、物理上出现的实际情形多半满足(τ₁)^1/2?α的条件,这时展开式收敛很快。对於二介质是重水和石墨的一个实例;我们算出了热能处中子慢化密度的数值结果(假定快中子源的能量为2兆电子伏),并和用通常二群近似方法求得的结果进行了比较。     

100Mo(n2n)99Mo,96Mo(n,p)96Nb和92Mo(n,α)89m+gZr反应截面测量

本文报告了在E_n=13.40—14.79MeV中子能区用活化法以²⁷Al(n,α)²⁴Na截面为中子注量标准测行的¹⁰⁰Mo(n2n)⁹⁹Mo,⁹⁶Mo(n,p)⁹⁶Nb和⁹²Mo(n,α)^89m+gZr的反应截面,中子能量是用铌锆截面比法测定的.文中将实验测量值与理论计算值进行了比较,还对上述三个反应的截面进行了编评,给出了推荐的激发曲线.     

中子平面晶体谱仪的分辨宽度

本文分析了中子平面晶体谱仪的分辨宽度,给出它的近似表示式为:△θ=((α₁²α₂²+α₁²β²+α₂²β²)/(α₁²+4β²+α₂²))^1/2;同时对几种常见情况也作了简略的讨论。为了确定计算参量△θ,又给出了晶体摇动曲线半宽度的近似表示式为:△γ=1/2(α₁²+4β²+α₂²)^1/2。以上两式中的α₁,α₂是第一、第二准直器的散开角;β是晶体单色器嵌镶结构(mosaic)分布半宽度。最后,依据上述结果,计算了我们仪器的分辨宽度,另外从该仪器测量的中子共振截面估计了它的分辨宽度,并作了比较。     

62Ni(n,α)59Fe反应截面测量

本文报告了在E_n=13.6—14.8MeV中子能区用活化法以²⁷Al(n,α)²⁴Na截面为中子注量标准测得的⁶²Ni(n,α)⁵⁹Fe的反应截面.在E_n为 13.64,13.79,14.00,14.05,14.33,14.60和14.80MeV处的截面分别为17.4±1.1,19.5±1.5,21.9±1.9,22.4±1.6,25.4±1.4,26.1±1.1和26.0±1.1mb.在文章中还列举了所能收集到的一些作者的数据以作比较.中子能量是用铌锆截面比法测定的.     

中子与α相互作用的两体等效可分离势

本文提供了一种n与α相互作用的等效两体可分离势,并给出了n-α散射的S_1/2,P_1/2,P_3/2分波相移对入射中子动能的解析表达式.用它计算各种动能的中子微分截面和极化都比较方便,计算结果与20MeV以下的中子散射实验数据作了比较,它们符合得很好.     

63Cu(n,α)60Co反应截面测量

本文报告了E_n=13.6—14.8MeV中子能区用活化法以²⁷Al(n,α)²⁴Na截面为中子注量标准得的⁶³Cu(n,α)⁶⁰Co的反应截面.在中子能量为13.64,13.79,14.03,14.33,14.60和14.80MeV的截面值分别为58.3±3.1,56.3±2.4,53.4±2.0,50.8±1.9,48.4±1.7和47.4±1.7mb.在文中还列举了一些作者的数据以作比较.中子能量是用铌锆截面比法测定的.     

α-碘酸锂的介电和导电行为

在沿c轴方向(以下简称c向)加静电场的作用下,测试频率为1OkHz时,测量了α-碘酸钾的表观介电系数ε′_c和ε′_a随同号电压V₊和异号电压V_-变化的特征曲线,确定了晶体中不存在类似于半导体的肖脱基阻挡层。当静电场加在c向上后,ε′_c变化的弛豫过程,与静电场作用下中子衍射强度增加的弛豫过程相似。实验观察到,这一晶体导电的载体主要是锂离子,并近似地具有在c向上一维电导性的特点。测出了c向电阻率ρ_c与V₊和V_-的特征曲线。     

任意阶球谐函数法求解辐射传输问题的误差分析

针对各向异性散射介质内的红外辐射传输开展数值方法研究.应用球谐函数展开推导了一维吸收、发射、散射性灰介质的辐射传输近似方程组,采用差分方法结合三对角矩阵解法建立了任意阶辐射传输近似方程数值解法.并通过计算算例验证了高阶PN方法的数值无关性问题.计算结果表明,高阶球谐函数数值解与理论解吻合得很好,同时计算验证了不同展开阶...     

各向异性非线性介质平板波导中的TM波

本文讨论了在三层平板介质波导中TM₀模的传播问题.三层介质的芯区是一层各向异性的Kerr型介质,上下两层则是线性介质.本文将利用E_x² >> E_x²这一性质,求解非线性方程组,给出零级近似和1级近似的解析解.     

60Ni(n,p)60Co反应截面测量

本文报告了E_n=13.6—14.8MeV中子能区用活化法以²⁷Al(n,α)²⁴Na截面为中子注量标准得的⁶⁰Ni(n,p)⁶⁰Co的反应截面.在E_n为 13.64,13.79,14.03,14.33,14.60,14.80MeV处的截面分别为184.4±12.2,178.8±10.5,171.4±10.3,161.9±9.6,157.0±9.3,147.5±8.9mb.在文章中还列举了所能收集的一些作者的数据以作比较.中子能量是用铌锆截面比法则定的.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Application of the modified differential approximation for radiative transfer to arbitrary geometry

The first-order spherical harmonics method (or P₁ approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P₁ approximation deteriorates as the optical thickness of the medium is decreased. The modified differential approximation (MDA) was originally proposed to remove the shortcomings of the P₁ approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results. The accuracy of MDA was found to be superior to the P₁ approximation for all optical thicknesses. Its accuracy, when compared with the discrete ordinates method (both S₆ and S₈), was found to be clearly superior in optically thin situations, but problem dependent in optically intermediate and thick situations. For 3D geometries, calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint. Several strategies to reduce both memory and computational time are discussed and demonstrated.     

Comparison of radiative transfer approximations for a highly forward scattering planar medium

We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P₃-approximations yield accurate results compared to solutions based on the F_N-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized.     

Anisotropic multiple scattering of collimated irradiance

Spherical harmonics are often used to solve multi-scatter transport problems. For a collimated incident beam, we describe a technique similar to the familiar P_N approximation except that we manage the infinite set of coupled equations in a novel way that permits the use of hundreds of harmonics to represent very pointed angular distributions. We split some equations into two approximate ones that depend on the angle of incidence. For plane slab geometry, the harmonics of low degree are solved in a coordinate system aligned to the boundary while the high harmonics use coordinates pointed at the source. We illustrate the technique with an extreme example: a scattering function having an integrable singularity in the forward direction. We give a time-dependent example along with several time-independent ones.     

典型时空中的运动效应和宇观红移现象

本文从相对性原理和局部光速不变性出发,建立了典型时空D_λ(1,4)的模型,讨论了其中的运动效应,计算了光谱线的频移,并在均匀分布的假定下与类星体N-Z关系的观测资料进行了比较。结果表明,河外天体的大红移可能主要不是由多普勒效应引起的,而在相当大程度上是典型时空中的距离效应。这样,运动群为SO(3,2)的模型D_λ<0(1,4)就可能是宇观时空较好的模写。     

耗散量子隧道系统中的形变效应与耦合指数的关系

采用变分方法，比较了超欧姆耗散两能态系统中位移变分态和位移－压缩变分态的特性。通过研究发现，在强耦合区域，位移－压缩态较稳定，其基态性质不仅取决于谱密度，而且还依赖于耦合强度ｇ₁～ω₁^λ的指数λ；位移－压缩态稳定的区域将随λ减小而增加。对于欧姆耗散两能态系统，在位移－压缩态退局域相区域亦有同样的特性，且该区域亦随λ减小而增加。 关键词：     

Effective response in nonlinear spherical coated composites under external AC and DC electric field

By using the perturbation method, effective nonlinear direct current (DC) and alternating current (AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of external electric field E_a =E₀ +E₁ sin ωt+E₃ sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Robust and accurate filtered spherical harmonics expansions for radiative transfer

We present a novel application of filters to the spherical harmonics (P_N) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme. The method is readily applied to existing codes that solve the P_N equations. Numerical results demonstrate that the solution to the filtered P_N equations are (i) more robust and less oscillatory than standard P_N solutions and (ii) more accurate than discrete ordinates solutions of comparable order. In particular, the filtered P₇ solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem in 2D Cartesian geometry.     

Asymptotic perturbation expansion in theP(φ)2 quantum field theory

In theP(φ)₂ model it is proved that the perturbation series for the infinite volume Schwinger functionsS(λ) are asymptotic in the limit as the coupling constant λ goes to zero. We also give conditions which imply smoothness ofS(λ) at arbitrary λ.     

Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous,anisotropically scattering media

Radiative transfer in a three-dimensional rectangular enclosure containing radiatively participating gases and particles is studied using the first- and third-order spherical harmonics approximations. Inhomogeneities in the radiative properties of the medium, as well as in the radiation characteristics of the boundaries, are allowed for. The scattering phase function is represented by the delta-Eddington approximation, and it is assumed to be a function of the location in order to account for density variation of the particles in the medium. Numerical solutions of the model equations are obtained using a finite difference scheme. For the purpose of validating the P₃-approximation, the results are compared with those based on Hottel's zonal method.