An error-free algorithm to solve a linear system of polynomial equations

The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors.     

Third order residual distribution schemes for the Navier–Stokes equations

We construct a third order multidimensional upwind residual distribution scheme for the system of the Navier–Stokes equations. The underlying approximation is obtained using standard P² Lagrange finite elements. To discretise the inviscid component of the equations, each element is divided in sub-elements over which we compute a high order residual defined as the integral of the inviscid fluxes on the boundary of the sub-element. The residuals are distributed to the nodes of each sub-element in a multi-dimensional upwind way. To obtain a discretisation of the viscous terms consistent with this multi-dimensional upwind approach, we make use of a Petrov–Galerkin analogy. The analogy allows to find a family of test functions which can be used to obtain a weak approximation of the viscous terms. The performance of this high-order method is tested on flows with high and low Reynolds number.     

Micro-segregation model calculation of residual tin in boiler and pressure vessel steel

Tin is a typical residual element in steel and mainly originates from Sn-containing complex iron ore and steel scrap. The segregation of Sn in steel is harmful to the performances of steel. In this paper, the micro-segregation of residual element Sn during the solidification process of boiler and pressure vessel steel by micro-segregation model was studied. The results showed that the micro-segregation degree of Sn reduces apparently with the increase of cooling rate and remarkably deteriorates during the solidification process. When the initial content of C is higher than 0.1%, it will cause the solidification transform of the solid phase converting from the ferrite phase to austenite phase and the significant increase in the micro-segregation degree of Sn. However, increasing the initial contents of Si, Mn, P and S separately has non-significant effects on the micro-segregation degree of Sn. In addition, the improvement of initial content of Sn will lead to the micro-segregation degree decrease of Sn and has an inapparent impact on zero strength temperature and zero ductility temperature of the boiler and pressure vessel steel.     

Adjustment of Residual Stresses in Unsymmetric Fiber-Reinforced Composites Using Genetic Algorithms

During the manufacturing process of multilayered fiber-reinforced composites with variable fiber orientations, residual stresses build up in these composites due to the directional expansion of single unidirectionally reinforced layers. Depending on the laminate lay-up, the inhomogeneous residual stresses, which are caused by thermal effects, moisture absorption, and chemical shrinkage, can lead to large multistable out-of-plane deformations. Instead of avoiding these curvatures, they can be advantageously used for technical applications following the near-net-shape technology. In order to adjust the deformations to the technical requirements, genetic algorithms in combination with a nonlinear calculation method have been developed, which can purposefully adapt the laminate lay-up depending on the loading and process parameters.     

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew [In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles, Int. J. Impact Eng. 19 (8) (1997) 715–726] are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 2.3 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. The simulation, performed using AUTODYN 2-D, assesses three numerical schemes, namely Langrange, Euler–Lagrange coupling and smooth particles hydrodynamics SPH–Lagrange coupling, in predicting the maximum depth of penetration and the radial stress–time response of the concrete target. When assessing the three solution techniques we hypothesize that the effect of strain rate on strength for the concrete target does not adversely affect the prediction on the maximum depth of penetration and the radial stress–time response of the concrete target. In the empirical approach the penetration equation developed by Forrestal et al. [An empirical equation for penetration depth of ogive-nose projectiles into concrete targets, Int. J. Impact Eng. 15 (4) (1994) 395–405] is used to determine the maximum depth of penetration and the deceleration–time response. The deceleration–time response for the projectile using the empirical approach is compared with those obtained from the numerical simulations. Results from both the numerical and empirical approaches are consistent. The calculated depth of penetration from both approaches yield relatively good agreement with that obtained from the experiment. The numerical simulations using each of the three numerical schemes are also able to reproduce the profiles from the radial stress measurements. Simulations using the SPH numerical scheme give the best overall agreement. The good overall agreement with the experimental radial stress measurements and consistent results between both empirical and numerical approach, enhanced the confidence in engineers and ballisticians when using these two approaches in complementing full-scale testing.     

Fluid phase topology of ethanol+benzene+cyclohexane at 101.3 kPa

In this article, isobaric vapor–liquid equilibria for the ternary mixture of ethanol?+?benzene?+?cyclohexane was experimentally investigated at atmospheric pressure. Vapor–liquid equilibria data for ethanol?+?benzene?+?cyclohexane at 101.3?kPa were obtained with a Othmer-type ebulliometer. Data were tested and considered thermodynamically consistent. The experimental results showed that this ternary mixture is completely miscible and exhibits three binary homogeneous azeotropes and a ternary minimum azeotrope at the studied conditions. Satisfactory results were obtained for correlation of equilibrium compositions with UNIQUAC activity coefficients model and also for prediction with UNIFAC method. In both cases, low root mean square deviations of vapor mole fraction and temperature were calculated. The capability of ethanol as modified distillation agent at atmospheric condition is discussed in terms of the thermodynamic topological analysis. However, owing to the complex topology of the ternary mixture it leads to a distillation scheme with three columns and difficult operation and thus, ethanol is not recommended as a separating agent for benzene?+?cyclohexane azeotrope.     

Digital photoelasticity of glass: A comprehensive review

The recent advances in digital photoelasticity have made it possible to use it conveniently for the stress analysis of articles and components made of glass. Depending on the application, the retardation levels to be measured range from a few nanometres to several thousand nanometres, which necessitates different techniques and associated equipments. This paper reviews the recent advances in the photoelasticity of glass with a focus on the techniques/methods developed in the last decade. A brief introduction to the residual stress in glass is provided initially to bring out its tensorial nature. The subsequent sections are organised thematically rather than chronologically, for better readability and easy access of information.     

Direct electron transfer reaction of glucose oxidase at bare silver electrodes and its application in analysis

The direct electron transfer reaction of glucose oxidase (GOx) at a bare silver electrode is verified. The electron transfer number n = 2, electron transfer coefficient α = 0.45 and rate constant of the electrochemical reaction K_s = 0.1 s⁻¹ are obtained. This communication presents a multimolecular adsorption model to explain the properties of the direct electron reaction between GOx and bare silver electrodes. The residual valence force may be an important factor to ensure a direct electron transfer reaction on the bare electrode. On the basis of the experimental fact that only biologically active GOx exhibits electrochemical activity in solution, a facile analytical method for analyzing the active GOx concentration is developed. The results determined correspond very well to that of a spectrometric method.     

电感耦合等离子发射光谱法测定渣油中铁、镍、钙、镁、钠、钒金属元素

用电感耦合等离子发射光谱法（ICP-AES）测定渣油中金属元素铁、镍、钙、镁、钠、钒，考察了不同的酸浓度对分析结果的影响和共存元素间的相互干扰，进行了加标回收率和精密度试验。     

Improving quantitative gas chromatography-electron ionization mass spectrometry results using a modified ion source: demonstration for a pharmaceutical application

Gas chromatography-mass spectrometry is a well established analytical technique. However, mass spectrometers with electron ionization sources may suffer from signal drifts, hereby negatively influencing quantitative performance. To demonstrate this phenomenon for a real application, a static headspace-gas chromatography method in combination with electron ionization-quadrupole mass spectrometry was optimized for the determination of residual dichloromethane in coronary stent coatings. Validating the method, the quantitative performance of an original stainless steel ion source was compared to that of a modified ion source. Ion source modification included the application of a gold coating on the repeller and exit plate. Several validation aspects such as limit of detection, limit of quantification, linearity and precision were evaluated using both ion sources. It was found that, as expected, the stainless steel ion source suffered from signal drift. As a consequence, non-linearity and high RSD values for repeated analyses were obtained. An additional experiment was performed to check whether an internal standard compound would lead to better results. It was found that the signal drift patterns of the analyte and internal standard were different, consequently leading to high RSD values for the response factor. With the modified ion source however, a more stable signal was observed resulting in acceptable linearity and precision. Moreover, it was also found that sensitivity improved compared to the stainless steel ion source. Finally, the optimized method with the modified ion source was applied to determine residual dichloromethane in the coating of coronary stents. The solvent was detected but found to be below the limit of quantification.