抽样法与灵敏度法k_(eff)不确定度量化

核反应堆的中子学模拟计算中,核数据的不确定度导致的积分量计算结果的不确定度,通常采用基于微扰理论的灵敏度与不确定度分析方法 (简称灵敏度法)量化.灵敏度分析法原则上只适用于线性模型,且一般输运计算程序难以直接进行灵敏度分析.而抽样法直接抽样核数据输入中子学计算程序进行计算,通过对计算结果的统计分析评估计算量的不确定度.抽样法易于实现、计算精确、且适用性强.在灵敏度分析与不确定度量化程序SURE中,增加了抽样法不确定度的量化功能.为将抽样法不确定度量化应用于复杂问题的模拟计算,需对其进行细致的考核.为此,选取简单的临界基准实验模型,分别采用灵敏度分析法和抽样法进行不确定度量化,得到了各核素各反应道核数据导致的k_(eff)计算不确定度.对比显示,两种方法的不确定度计算结果有很好的符合,验证了SURE程序抽样法功能的正确性.抽样法计算的k_(eff)符合正态分布,说明在一般核数据的不确定度范围内,k_(eff)与核数据近似成线性关系,利用灵敏度分析法评估k_(eff)计算值的不确定度是适用的.     

辐射不透明度计算中含温有界原子结构理论的不确定度量化

以交换势的泛函表达式为核心,分析产生原子结构理论不确定度的主要原因,阐述辐射不透明度计算中含温有界原子结构理论不确定度量化的具体步骤,给出能级、矩阵元的不确定度量化计算公式,以及判定理论模型优劣的判据.以汞、金、铁元素为例,通过数值计算,根据对比分析,验证该不确定度量化方法的可行性.     

ICP-AES分析茶叶中Mg和K含量的不确定度评定

对用电感耦合等离子体-原子发射光谱法(ICP-AES)测定茶叶中的金属元素Mg、K含量的不确定度来源进行分析和计算.其分析方法的标准不确定度主要来源包括物质称量、线性回归拟合、溶液稀释等过程,并依据不确定度的评定方法计算各不确定度分量,结果表示茶叶中Mg、K的含量依次为1773、16666mg/kg,标准不确定度依次为...     

碱萃取比色法测定塑胶粒中Cr（Ⅵ）含量的不确定度分析

应用EPA3060A碱萃取方法和EPA7196A二苯碳酰二肼分光光度法(比色法)测定塑胶粒中Cr(Ⅵ)含量,通过建立测试数学模型,确定不确定的来源,分析Cr(Ⅵ)测定不确定度,不确定度主要由样品质量称量、结果重复性测试、示踪液的回收率、校准曲线拟合、配制校准曲线溶液浓度、待测溶液定容等产生的测量不确定度,计算合成标准不确定度为0.06mg/kg,扩展不确定度为0.12mg/kg.     

石墨炉原子吸收光谱法测定水样中钒的不确定度评定

采用石墨炉原子吸收光谱法(GFAAS)对水样中的钒进行测定,其测量不确定度主要来源于标准溶液配制、曲线拟合、样品的准备和重复测量.并对各个不确定度分量进行了评估和量化计算,得出标准不确定度和扩展不确定度.当水样中钒的含量为4.68μg·L-1时,其扩展不确定度为0.18μg·L-1(k=2).该不确定度表示方法在实际工作中具有较好的实用价值.     

爆轰模拟不确定度的量化方法

通过对数值模拟不确定度产生机制的理论分析以及对不确定度从考核区到应用区发展趋势的反演,展示数值模拟不确定度量化评估的关键技术.基于工程设计的现实需求和数值模拟中验证与确认的思想,提出数值模拟用于对爆轰系统进行科学预测时不确定度的评估框架,并结合实例对方法进行演示和验证.     

校准条件下的数值模拟不确定度量化方法

当存在众多不确定输入因素时,不确定度的传递分析往往导致对数值模拟不确定度的过高估计.利用校准行为能够消减系统级数值模拟中认知不确定度的客观机制,提出一个综合利用已有系统级试验对比信息和新增建模与模拟传递信息的不确定度量化方法,结合一个虚拟试验的例子对该方法进行展示和验证.     

容量法测定硫酸镁注射液含量的不确定度评定

讨论了容量法测定硫酸镁注射液含量中的各种不确定度影响因素。通过对测定过程中各种影响因素进行分析评估,计算出各分量的不确定度,得出合成不确定度和扩展不确定度(k=2)。建立的不确定度计算方法适用于容量法测定硫酸镁注射液含量的不确定度评价。     

ICP-MS测量溶液中痕量Sm的不确定度评定

为了更合理、科学地表示测量结果 ,本文按照 GUM和国家质量技术监督局颁布的计量技术规范 ,对电感耦合等离子体 -质谱 (ICP- MS)测量溶液中痕量 Sm的不确定度进行了评定 ,提供了计算过程所需各参数的采集和计算方法 ,评定了各标准不确定度分量、合成标准不确定度、自由度和扩展不确定度。此方法还可为类似仪器测量结果不确定度的评定提供参考。     

颜色温度和相关色温的不确定度评定方法

颜色温度和相关色温是光源的重要参量。从色品坐标(u,v)到颜色温度和相关色温的计算过程比较复杂,很难依据国际标准化组织推荐的不确定度评定方法进行分析。介绍了从光谱辐射功率和色品坐标(u,v)的不确定度出发,按照国际标准化组织的推荐方法,得到更为科学合理的颜色温度和相关色温的不确定度评定方法。针对新的国家颜色温度副基准,分别采用基于数学模型的精确方法、近似方法和几何方法对其不确定度进行了评价,并与传统方法进行了比较。采用传统方法得到的计算结果偏高,这是因为传统的计算方法很大程度上基于实验和经验估计,没有将颜色温度的不确定度与光谱辐射功率和色品坐标(u,v)的不确定度之间建立明确的数学关联,在分析过程中存在对某一不确定度源进行重复计算的可能。所述的数学推导方法相对传统方法更为科学合理。     

Asymptotic freedom,infrared convergence and supersymmetry

The conditions for infrared convergence and asymptotic freedom are investigated for a system in which (in order to produce a spontaneous breakdown) a supersymmetric matter-matter interaction is added to the supersymmetric Yang-Mills Lagrangian. It is found that, in contrast to conventional theory, the conditions imposed by the asymptotic freedom of the matter-matter interaction are not stringent, and are automatically satisfied for adjoint representations. The conditions for infrared convergence are also not too stringent. However the joint conditions for asymptotic freedom and infrared convergence turn out to be quite stringent. Nevertheless, a model is proposed which, subject to some reservations, appears to satisfy the joint conditions.     

On Symplectic and Multisymplectic Structures and Their Discrete Versions in Lagrangian Formalism

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively.We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire grometric object and the noncommutative differential calculus on regular lattice.In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations,the Euler-Lagrange cohomological concepts and content in the configuration space are employed.     

Fully implicit 1D radiation hydrodynamics: Validation and verification

A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tridiagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry. Results obtained when radiation interaction is also accounted agree with those of point explosion with heat conduction for lower input energies. Having, thus, benchmarked the code, self convergence of the method w.r.t. time step is studied in detail for both the planar and spherical problems. Spatial as well as temporal convergence rates are ?1 as expected from the difference forms of mass, momentum and energy conservation equations. This shows that the asymptotic convergence rate of the code is realized properly.     

Convergence Speed for Simple Symmetric Exclusion: An Explicit Calculation

For the infinite-volume simple symmetric nearest-neighbor exclusion process in one dimension, we investigate the speed of convergence to equilibrium from a particular initial distribution. We use duality to reduce the analysis to that of the two-particle process, which we further reduce to a random walk reflecting rightward at zero, whose generator is self-adjoint on l ²(Z). We obtain the spectral representation of the generator and use asymptotic analysis to show that convergence is slow.     

Theory of neutrino masses and mixing

We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and discuss their applications. We exemplify these theoretical concepts with the groups S ₄ and A ₄. Finally, we discuss the relation between tensor products of irreducible representations and Yukawa couplings and describe a model for tri-bimaximal lepton mixing based on A ₄.     

Discrete Velocity Fields with Explicitly Computable Lagrangian Law

We introduce a class of random velocity fields on the periodic lattice and in discrete time having a certain hidden Markov structure. The generalized Lagrangian velocity (the velocity field as viewed from the location of a single moving particle) has similar hidden Markov structure, and its law is found explicitly. Its rate of convergence to equilibrium is studied in small numerical examples and in rigorous results giving absolute and relative bounds on the size of the second–largest eigenvalue modulus. The effect of molecular diffusion on the rate of convergence is also investigated; in some cases it slows convergence to equilibrium. After repeating the velocity field periodically throughout the integer lattice, it is shown that, with the usual diffusive rescaling, the single–particle motion converges to Brownian motion in both compressible and incompressible cases. An exact formula for the effective diffusivity is given and numerical examples are shown.     

On convergence,asymptotic behaviour and computational algorithm of generalized exponential integral functions arising in a radiative transfer

In this paper, we investigate uniform convergence of the generalized exponential integral functions (GEI) arising in the study of radiative transfer in a two-dimensional planar-medium and anisotropic scattering in a multidimensional medium. Using the uniform convergence, we study the properties and asymptotic behaviour of the GEI functions. We also give an efficient algorithm for the computations of the values of the GEI functions.     

Brachistochrones in potential flow and the connection to Darwin's theorem

We establish the existence and the asymptotic properties of a path of minimum travel time for a line of particles starting upstream of a sphere or cylinder in potential flow. A connection is made between this brachistochrone path and Darwin's proposition which relates the added mass with the drift volume dragged by a body moving an infinite distance in the fluid. We compute an asymptotic correction to the drift volume for finite distances and show how the brachistochrone path is connected to the reflux volume. We present accurate numerical calculations for the brachistochrone position, point of zero horizontal Lagrangian displacement, reflux and partial drift volumes. These calculations are seen to agree well with the asymptotic predictions even for moderate values of the parameters. In the small Reynolds number regimes, we show that while for the case of Stokes flow past a sphere no brachistochrones exist at finite distances from the sphere, the Oseen correction is sufficient to restore such least-time trajectories. Lastly, the application to a sphere falling in a stratified fluid is discussed using the new drift volume correction formula.     

Vacuum polarization induced by the intense gauge field

The results obtained from consideration of the effective Lagrangian density asymptotic behaviour in gauge theories by means of the renormalization-group method are discussed. Such a consideration allows one to relate the asymptotic behaviour of the effective Lagrangian density in strong fields to the short-range behaviour of gauge theories.     

Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach

The linear operator plays an important role in the computational process of Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can be chosen to develop a solution. Hence, it is easy to introduce the modified/physical parameter dependent linear operators. The effective use of these operators has been judged through solving fluid flow problems. Modification in linear operators affects the solution and improves the computational efficiency of HAM for larger values of parameters. The convergence rate of the solution is rapid and several times higher resulting in less computational time.