Light Element Analysis of Individual Microparticles Using Thin-Window EPMA

 The determination of the concentration of light elements, such as carbon, nitrogen and oxygen, in e.g. atmospheric aerosol particles is important to study the chemical behaviour of atmospheric pollution. The knowledge of low-Z element concentrations gives us information on the speciation of nutrients (species having nutritional value for plants) and toxic heavy metals in the particles. The capability of the conventional energy-dispersive EPMA is strongly limited for the analysis of low-Z elements, mainly because the Be window in the EDX detector hinders the detection of characteristic X-rays of light elements such as C, N, O and Na. WDS is suitable for analysis of light elements, but the measurement of beam sensitive microparticles requires the minimisation of the beam current and the measurement time. A semi-quantitative analytical method based on EPMA using an ultra-thin window EDX detector was developed. It was found that the matrix and geometric effects that are important for low-energy X-rays can be reliably evaluated by Monte Carlo calculations. Therefore, the quantification part of the method contains reverse Monte Carlo calculation done by iterative simulations. The method was standardised and tested by measurements on single particles with known chemical compositions. Beam-sensitive particles such as ammonium-sulphate and ammonium-nitrate were analysed using a liquid nitrogen cooled sample stage. The shape and size of the particles, which are important for the simulations, were determined using a high-magnification secondary electron image. Individual marine aerosol particles collected over the North Sea by a nine-stage Berner cascade impactor were analysed using this new method. Preliminary results on five samples and 4500 particles show that the method can be used to study the modification of sea-salt particles in the troposphere.     

A time-stepping procedure based on convolution for the mixed finite element approximation for porous media flow

A time-stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post-processed by the convolution with Bramble-Schatz kernel. Convergence analysis shows that the property of superconvergence, originally held for the approximation of velocity, can be retained for the approximation of concentration variable. Compared with the traditional results in references, the constraint conditions between parameters in this paper are improved essentially.     

Analysis for Transmission Characteristics of Closed Trapezoidal-Groove Waveguide with Boundary Element Method

In this paper, the cut-off and dispersion characteristics of a new kind of closed trapezoidal-groove waveguide that has more advantages than open groove waveguides are analyzed with the help of the boundary element method, the relationship between cut-off wavelengths and variations of guide's relative sizes is discussed in detail. The calculated results are in good agreement with those in the relevant reference. So, the obtained conclusions are very important in theoretical studies and actual applications of closed trapezoidal-groove waveguides for millimeter and submillimeter waves.     

New mixed finite elements for plane elasticity and Stokes equations

We consider mixed finite elements for the plane elasticity system and the Stokes equation. For the unmodified Hellinger-Reissner formulation of elasticity in which the stress and displacement fields are the primary unknowns, we derive two new nonconforming mixed finite elements of triangle type. Both elements use piecewise rigid motions to approximate the displacement and piecewise polynomial functions to approximate the stress, where no vertex degrees of freedom are involved. The two stress finite element ...     

A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows

We address the failure in scalability of large-scale parallel simulations that are based on (semi-)implicit time-stepping and hence on the solution of linear systems on thousands of processors. We develop a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources. It is a non-intrusive approach as it does not require modification of existing codes. Specifically, we present here a two-stage domain decomposition method for the Navier–Stokes equations that combines features of discontinuous and continuous Galerkin formulations. At the first stage the domain is subdivided into overlapping patches and within each patch a C⁰ spectral element discretization (second stage) is employed. Solution within each patch is obtained separately by applying an efficient parallel solver. Proper inter-patch boundary conditions are developed to provide solution continuity, while a Multilevel Communicating Interface (MCI) is developed to provide efficient communication between the non-overlapping groups of processors of each patch. The overall strong scaling of the method depends on the number of patches and on the scalability of the standard solver within each patch. This dual path to scalability provides great flexibility in balancing accuracy with parallel efficiency. The accuracy of the method has been evaluated in solutions of steady and unsteady 3D flow problems including blood flow in the human intracranial arterial tree. Benchmarks on BlueGene/P, CRAY XT5 and Sun Constellation Linux Cluster have demonstrated good performance on up to 96,000 cores, solving up to 8.21B degrees of freedom in unsteady flow problem. The proposed method is general and can be potentially used with other discretization methods or in other applications.     

Boundary element method for calculation of effective elastic moduli in 3D linear elasticity

A boundary integral formulation of the linear elasticity problem for a multi‐component composite is given. The fast BEM solver based on the adaptive cross approximation is then obtained by the data‐sparse representation of the resulting Galerkin matrices. The solver is used to obtain effective elastic moduli of fibre and particle reinforced composites in three dimensions by means of the strain energy equivalence principle. Copyright © 2009 John Wiley & Sons, Ltd.     

A finite strain contact model for mixed lubricated surfaces in forming processes

For an accurate simulation of forming processes, it is of paramount importance to model the different lubrication regimes that can develop at the contact interface. These might vary from zone to zone of the forming piece, and from one regime to another, resulting in forces of different nature and magnitude. In these cases, the use of the classical Coulomb friction law will be clearly not sufficient to capture, in a suitable manner, the variety of forces applied on the forming piece.     

二阶Dirichlet问题的三维等参元逼近及其数值积分格式

本文研究了求解三维二阶Drichlet问题的四面体等参元逼近格式.基于对等参变换的细致估计,证明了格式的收敛性,并得到了H~1-误差的最优估计.为简化等参元的复杂计算,本文还构造了一种简单的数值积分格式,并证明了其收敛性.     

A POSTERIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE CAHN-HILLIARD EQUATION AND THE HELE-SHAW FLOW

This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut ＋ △（ε△Au-ε^-1f（u）） = 0. It is shown that the a posteriori error bounds depends on ε^-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct at2 adaptive algorithm for computing the solution of the Cahn- Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.     

Simulating hydrostatic and non‐hydrostatic oceanic flows

The thin aspect ratio of oceanic basins is simultaneously a complication to contend with when developing ocean models and an opportunity to simplify the equations of motion. Here we discuss these two aspects of this geometric feature in the context of hydrostatic and non‐hydrostatic ocean models. A simple analysis shows that the horizontal viscous operator in the hydrostatic primitive equations plays a central role in the specification of boundary conditions on the lateral vertical surfaces bounding the domain. The asymptotic analysis shows that for very thin aspect ratios the leading‐order flow cannot be closed unless additional terms in the equations are considered, namely either the horizontal viscous forces or the non‐hydrostatic pressure forces. In either case, narrow boundary layers must be resolved in order to close the circulation properly. The computational cost increases substantially when non‐hydrostatic effects are taken into account. Copyright © 2008 John Wiley & Sons, Ltd.