Resolving uncertainty in chemical speciation determinations

Speciation determinations involve uncertainty in system definition and experimentation. Identification of appropriate metals and ligands from basic chemical principles, analytical window considerations, types of species and checking for consistency in equilibrium calculations are considered in system definition uncertainty. A systematic approach to system definition limits uncertainty in speciation investigations. Experimental uncertainty is discussed with an example of proton interactions with Suwannee River fulvic acid (SRFA). A Monte Carlo approach was used to estimate uncertainty in experimental data, resulting from the propagation of uncertainties in electrode calibration parameters and experimental data points. Monte Carlo simulations revealed large uncertainties present at high (>9–10) and low (<4) −log[H⁺], which result from larger instabilities in the proton balance function in these regions. Uncertainties in speciation parameters were compared for uniresponse fitting (linear programming and least-squares) and multiresponse fitting. Linear programming and least-squares approaches both fit the observed data, but suggest different mixtures of monoprotic ligands. Least-squares fit the data with 21 sites, whereas linear programming fit the data equally well with 9 sites. Multiresponse fitting, involving simultaneous fluorescence and pH measurements, improved model discrimination. Deconvolution of the excitation versus emission fluorescence surface for SRFA establishes a minimum of five sites. Diprotic sites are also required for the five fluorescent sites, and one non-fluorescent monoprotic site was added to accommodate the pH data. Consistent with greater complexity, the multiresponse method had broader confidence limits than the uniresponse methods, but corresponded better with the accepted total carboxylic content for SRFA. Overall there was a 40% standard deviation in total carboxylic content for the multiresponse fitting, versus 10% and 1% for least-squares and linear programming, respectively.     

A numerical method for the solution of the nonlinear turbulent one-dimensional free surface flow equations

Free surface flow of an incompressible fluid over a shallow plane/undulating horizontal bed is characteristically turbulent due to disturbances generated by the bed resistance and other causes. The governing equations of such flows in one dimension, for finite amplitude of surface elevation over the bed, are the Continuity Equation and a highly nonlinear Momentum Equation of order three. The method developed in this paper introduces the “discharge” variable q = η U, where η = elevation of the free surface above the bed level, and U = average stream-wise forward velocity. By this substitution, the continuity equation becomes a linear first-order PDE and the momentum equation is transformed after introduction of a small approximation in the fifth term. Next, it is shown by an invertibility argument that q can be a function of η: q = F(η), rendering the momentum equation as a first order, second degree ODE for F(η), that can be be integrated by the Runge-Kutta method. The continuity equation then takes the form of a first order evolutionary PDE that can be integrated by a Lax-Wendroff type of scheme for the temporal evolution of the surface elevation η. The method is implemented for two particular cases: when the initial elevation is triangular with vertical angle of 120 ^° and when it has a sinusoidal form. The computations exhibit the physically interesting feature that the frontal portion of the propagating wave undergoes a sharp jump followed by tumbling over as a breaker. Compared to other discretization methods, the application of the Runge-Kutta and an extended version of the Lax-Wendroff scheme is much easier.     

A new schedule for copper chemical speciation analysis in soil and water sediment

The speciation of heavy metals is very important to evaluate their environmental impact. This issue has become an interested topic many decades ago and many significative studies were carried out such as direct detecting, calculation with mathematical model represented in recent years as well as Tessier＇s work in 1979, BCR＇s work in 1993, etc. In all of them, the methods recommended by Tessier and BCR are most often used in practical study today. But it should be seen that experimental schedule and agents define these methods including BCR＇s method, which improved on Tessier＇s method, only. In many cases, there always are deviations between analytical results and real content of the speciation. Otherwise, steps of the extraction experiment are always strict and excessive in the experimental process. The method, which is fitting to extract the speciation of bioavailability and easy to assess the effect of metals in the environment, is very anticipant. In this paper, the sequential three steps schedule of speciation analysis of copper in soil and water sediment is discussed as an example based on the comparative results of experimental analysis with the schedules of BCR＇s （mended by Rauret et al. in 1999） and TDPA （diethylenetriamine pentacetic acid） extraction, respectively. The results from sequential three steps method and other methods recommended by prevenient work suggest that the analytical schedule of sequential three steps of separating speciation （the speciation of easy effect to life-form, the speciation available to life-form, and the speciation of no effect to life-form） is valuable for copper speciation analysis in soil and sediment. Because of easy process and saving time to evaluate its availability for life form,     

完全非线性聚焦波浪的数值模拟

利用高阶边界元方法求解拉普拉斯方程,建立了模拟完全非线性聚焦波的时域数值模型,其中追踪流体自由表面的方法为满足完全非线性自由水面条件的半混合欧拉-拉格朗日方法,运用四阶Runga-Kutta方法计算每一时间步新的波面高度和速度势,同时通过入射边界给定速度的二阶Stokes解析解产生波浪,并应用镜像格林函数消除水槽两个侧面和底面上的积分。对不同波陡的聚焦波群在水槽中开展了物理模型实验,并把试验结果和数值结果进行了对比,两者吻合得很好,然后对非线性条件下聚焦波的特点进行了研究。     

Distribution,chemical speciation and source of trace elements in surface sediments of the Changjiang Estuary

To evaluate biogeochemical characteristics, eco-environmental risks and sources of trace elements (TEs: As, Hg, Se, Sb, Te, Sn, Bi and Ge), their total concentrations and chemical speciation in surface sediments collected from the Changjiang Estuary were determined. Total concentrations for As, Hg, Se, Sb, Te, Sn, Bi and Ge were 4.57–30.20, 0.01–0.40, 0.04–0.38, 0.36–1.48, 0.02–0.10, 0.48–6.58, 0.13–0.64 and 0.83–2.43 μg/g, respectively, with higher values at the estuary. This distribution pattern was attributed to the riverine input and high clay and total organic carbon contents. The sequential extraction suggested that TEs mainly occurred in residual fractions. The risk assessment code suggested that As, Hg and Sn were at low risk, whereas Bi, Se, Sb, Te and Ge were at medium risk. The geoaccumulation index (I _geo) and principal component analysis indicated that Se and Sn mainly came from the natural input (crustal and biological inputs), whereas As, Sb, Hg, Bi and Te came from both of the crustal and anthropogenic inputs via atmosphere and rivers. In addition, Ge possibly came from the natural (crustal and biological inputs) and anthropogenic inputs.     

基于非达西渗流的软土一维非线性固结半解析解

在土中渗流遵循非达西渗流定律的前提下,考虑软土在固结过程中的非线性固结特性,根据饱和土体一维固结的连续条件,推导出基于非达西渗流的软土一维非线性固结控制方程。利用半解析方法对其进行求解,并与差分计算结果进行对比,验证半解析方法的可靠性。最后,着重分析非达西渗流与达西定律之间非线性固结性状的差别,以及不同自重应力分布方式对固结速率的影响。结果表明,考虑非达西渗流下的非线性固结速率比达西定律下要慢,且指数和临界水力坡降越大,非线性固结速率越慢。而且,作用的外荷载越小、地基土层越厚,非达西渗流下非线性固结速率的减慢愈明显。自重应力均匀分布下的非线性固结速率要比自重应力线性分布下慢,但随着荷载的增大、土层的变薄,两者之间的差别会越来越小。     

Performance of Jacobi preconditioning in Krylov subspace solution of finite element equations

This paper examines the performance of the Jacobi preconditioner when used with two Krylov subspace iterative methods. The number of iterations needed for convergence was shown to be different for drained, undrained and consolidation problems, even for similar condition number. The differences were due to differences in the eigenvalue distribution, which cannot be completely described by the condition number alone. For drained problems involving large stiffness ratios between different material zones, ill‐conditioning is caused by these large stiffness ratios. Since Jacobi preconditioning operates on degrees‐of‐freedom, it effectively homogenizes the different spatial sub‐domains. The undrained problem, modelled as a nearly incompressible problem, is much more resistant to Jacobi preconditioning, because its ill‐conditioning arises from the large stiffness ratios between volumetric and distortional deformational modes, many of which involve the similar spatial domains or sub‐domains. The consolidation problem has two sets of degrees‐of‐freedom, namely displacement and pore pressure. Some of the eigenvalues are displacement dominated whereas others are excess pore pressure dominated. Jacobi preconditioning compresses the displacement‐dominated eigenvalues in a similar manner as the drained problem, but pore‐pressure‐dominated eigenvalues are often over‐scaled. Convergence can be accelerated if this over‐scaling is recognized and corrected for. Copyright © 2002 John Wiley & Sons, Ltd.     

Methods for the numerical solution of the equations of viscoelasticity

In this paper a finite element formulation for a linear viscoelastic ageing material is developed. It is shown that these equations can be solved in the from of an eigenvalue expansion thus reducing the problem to the solution of a set of Volterra Integral equations. An alternative method of solution based on expansion in terms of an operator related to Poisson's ratio is also developed and this solution method is found to significantly reduce the computational effort necessary in the solution of aproblem.     

Geochemical kinetics via the Swift-Connick equations and solution NMR

Signal analysis in Nuclear Magnetic Resonance spectroscopy is among the most powerful methods to quantify reaction rates in aqueous solutions. To this end, the Swift-Connick approximations to the Bloch-McConnell equations have been used extensively to estimate rate parameters for elementary reactions. The method is primarily used for ¹⁷O NMR in aqueous solutions, but the list of geochemically relevant nuclei that can be used is long, and includes ²⁹Si, ²⁷Al, ¹⁹F, ¹³C and many others of particular interest to geochemists. Here we review the derivation of both the Swift-Connick and Bloch-McConnell equations and emphasize assumptions and quirks. For example, the equations were derived for CW-NMR, but are used with modern pulse FT-NMR and can be applied to systems that have exchange rates that are shorter than the lifetime of a typical pulse. The method requires a dilute solution where the minor reacting species contributes a negligible amount of total magnetization. We evaluate the sensitivity of results to this dilute-solution requirement and also highlight the need for chemically well-defined systems if reliable data are to be obtained. The limitations in using longitudinal relaxation to estimate reaction rate parameters are discussed. Finally, we provide examples of the application of the method, including ligand exchanges from aqua ions and hydrolysis complexes, that emphasize its flexibility. Once the basic requirements of the Swift-Connick method are met, it allows geochemists to establish rates of elementary reactions. Reactions at this scale lend themselves well to methods of computational simulation and could provide key tests of accuracy.     

A local solution for deterministic and stochastic transport equations

A local method is developed for finding the hydraulic head at an arbitrary point of a soil deposit with conductivity varying randomly in space. The method is said to be local since it delivers the hydraulic head at an arbitrary point of a soil deposit directly rather than extracting it from a field solution. The local method always converges to the exact solution, is ideal for parallel computation, and is simple to implement. The method is applied to solve locally one-dimensional transport equations with mixed boundary conditions, calculate corresponding effective conductivity, and examine size effect in specimens with hydraulic conductivity varying randomly in space.     

自适应非线性有限元的多重网格法求解及应用

描述了非线性自适应有限元的多重网格法求解过程。 通过算例说明了方法的有效性以及自适应多重网格有限元用于开挖施工过程模拟分析的优越性。     

Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control

Dissolution and precipitation rates of brucite (Mg(OH)₂) were measured at 25°C in a mixed-flow reactor as a function of pH (2.5 to 12), ionic strength (10⁻⁴ to 3 M), saturation index (−12 < log Ω < 0.4) and aqueous magnesium concentrations (10⁻⁶ to 5·10⁻⁴ M). Brucite surface charge and isoelectric point (pH_IEP) were determined by surface titrations in a limited residence time reactor and electrophoretic measurements, respectively. The pH of zero charge and pH_IEP were close to 11. A two-pK, one site surface speciation model which assumes a constant capacitance of the electric double layer (5 F/m²) and lack of dependence on ionic strength predicts the dominance of >MgOH₂⁺ species at pH < 8 and their progressive replacement by >MgOH° and >MgO⁻ as pH increases to 10-12. Rates are proportional to the square of >MgOH₂⁺ surface concentration at pH from 2.5 to 12. In accord with surface speciation predictions, dissolution rates do not depend on ionic strength at pH 6.5 to 11. Brucite dissolution and precipitation rates at close to equilibrium conditions obeyed TST-derived rate laws. At constant saturation indices, brucite precipitation rates were proportional to the square of >MgOH₂⁺ concentration. The following rate equation, consistent with transition state theory, describes brucite dissolution and precipitation kinetics over a wide range of solution composition and chemical affinity:

     

软土一维非线性固结近似解析解

软土非线性固结变形计算目前还主要依赖于数值方法,致使非线性固结理论的工程应用受到极大限制。引入经典的e-lg?' 和e-lgkv非线性关系,在自重应力均匀分布假定下通过变量代换并利用迭代法给出压缩指数Cc与渗透指数Ck比值不等于1时的非线性固结近似解析解。在Cc /Ck趋近1时本文解与其等于1时的差分解及精确解相差无几。但如果Cc /Ck值偏离1,该近似解会存在一定偏差,且偏差值会随Cc /Ck值偏离1的程度和外荷载增加而逐渐增大。在一般工程荷载作用下,如果Cc /Ck值介于0.9～1.1之间,本文解的平均固结度与差分解间最大偏差在2%左右。当Cc /Ck值在0.75～1.25之间时,本文解的平均固结度与差分解最大偏差在5%左右。如果Cc /Ck值在0.5～1.5之间,本文解的平均固结度与差分解间最大偏差在10%左右。当外荷载一定时,土层的非线性固结速率会随着Cc /Ck值的增大而减慢。如果Cc /Ck<1,土层的非线性固结速率会随外荷载的增大而加快;相反,如果Cc/Ck>1,土层的非线性固结速率会随外荷载增大而减慢。     

Numerical simulation of liquefaction in porous media using nonlinear fluid flow law

It is well known that for a sufficiently high seepage velocity, the governing flow law of porous media is nonlinear (J. Computers & Fluids 2010; 39 : 2069–2077). However, this fact has not been considered in the studies of soil‐pore fluid interaction and in conventional soil mechanics. In the present paper, a fully explicit dynamic finite element method is developed for nonlinear Darcy law. The governing equations are expressed for saturated porous media based on the extension of the Biot (J. Appl. Phys. 1941; 12 : 155–164) formulation. The elastoplastic behavior of soil under earthquake loading is simulated using a generalized plasticity theory that is composed of a yield surface along with non‐associated flow rule. Numerical simulations of porous media subjected to horizontal and vertical components of ground motion excitations with different permeability coefficients are carried out; while computed maximum pore water pressure is specially taken into consideration to make the difference between Darcy and non‐Darcy flow regimes tangible. Finally, the effect of non‐Darcy flow on the evaluated liquefaction potential of sand in comparison to conventional Darcy law is examined. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical solution for dynamics of pneumatic DTH hammer system

The pneumatic down-the-hole(DTH) hammer is one of the efficient equipments used in medium hard to very hard rock drilling frield,and any change in its structure design affects all performance parameters of a pneuamtic DTH hammer directly.Yet,owing to the complexity of the dynamic interaction among the components in DTH hammer systems,until now it has been difficult to obtain reliable estimates of the design parameter affects.Thus providing an design parameter optimization and the layout of dynamics behavior of DTH hammer is of great importance.This paper documents the development and solution of a computational model for the dynamic response of a pneumatic DTH hammer.The model consists of rigid piston dynamics equation and chamber thermodynamics equations.The resulting model represented by a set of coupled nonlinear differential equations were computed in Visual C++ program.The developed solutions are used to perform a parametric study to illustrate the inffluence of the piston mass and supply pressure on the impact performance of DTH hammer system.     

GeoPyTool:A cross-platform software solution for common geological calculations and plots

GeoPyTool is an open source application developed for geological calculations and plots,such as geochemical classification,parameter calculation,basic statistical analysis and diagrams for structural geology.More than acting as a link from raw data stored in Microsoft Excel~(?)(MS Excel)files to vector graphic files,GeoPyTool includes recently developed routines that have not been included in previous software,such as the calculation of the Ce~((Ⅳ))/Ce~((Ⅲ))ratio for zircons as a method to examine the temporal evolution of oxygen fugacity in the magmatic source for igneous rocks,and the temperature calculator with titanium in zircon and zirconium in rutile.Besides these routines,GeoPyTool also allows users to load any figure from articles or books as a base map.As a Python-based crossplatform program,GeoPyTool works on Windows~(?),MacOS X~(?)and GNU/Linux.GeoPyTool can do the whole process from data to results without the dependence of Microsoft Excel~(?),CorelDraw~(?) and other similar software.It takes Excel~(?)XLSX and CSV(Comma Separated Value)as the formats of both the input data source files and the output calculation results files.The figures generated by GeoPyTool can be saved as portable network graphics(PNG),scalable vector graphics(SVG)or portable document format(PDF).Another highlight of GeoPyTool is the multilingual support,the official versio n of GeoPyTool supports both Chinese and English,and additional languages can be loaded through interface files.GeoPyTool is still in the development stage and will be expanded with further geochemical and structural geology routines.As an open source project,all source code of GeoPyTool are accessible on Github(https://github.com/GeoPyTool/GeoPyTool).Users with Python experience can join in the development team and build more complex functions expanding the capabilities of GeoPyTool.     

Numerical solution for consolidation and desiccation of soft soils

The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd.     

浅水方程数值计算方法的研究

求解以水位为变量的连续方程,并根据Navier-Stokes方程压力修正算法的基本思想,建立了浅水方程的水位修正算法,放宽了对离散时间步长的限制.通过对离散方程系数矩阵的重新构造,建立了高分辨率有限元格式,该格式既具有较高的离散精度又避免了数值解的伪振荡.对动量方程的阻力项做负坡线性化处理,提高了露滩计算的稳定性.数值模拟结果与解析解吻合良好,表明所建立的数值计算方法是正确的和可靠的.     

A frequency-domain analytical solution of Maxwell's equations for layered anisotropic media

An analytical solution of Maxwell's equations for layered anisotropic media is presented in a form which allows estimating the sought parameters by layer stripping without round-off accumulation. The solution in each layer is reduced to the standard procedures of solving a fourth-order algebraic equation, multiplication, addition, and inversion of second-order non-singular matrices. The algorithm has no limitations on layer thickness and is applicable to both very thick and very thin layers. The new numerical code is straightforward and can be easily parallelized.