Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.     

STUDENT TEACHERS’ UNDERSTANDING OF RATIONAL NUMBER: PART-WHOLE AND NUMERICAL CONSTRUCTS

Previous research has shown that secondary school students’ understanding of fractions is dominated by the part-whole concept to the possible detriment of their understanding of a fraction as a number in its own right. The present paper reports on an investigation into the understanding of intending primary teachers in this area. Four representatives of a cohort of sixty students on a PGCE course specialising in the lower primary age range were asked detailed questions probing their knowledge of fractions. The conclusion was that the part-whole concept dominates. All of the students were familiar with the numerical concept from their work on the PGCE course, but they reverted to the more familiar part-whole ideas in attempting to solve problems.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

Continuous Spectroscopy Characterization of Emulsions

In emulsion polymerization, the formation of particles has an important effect on the rate of reaction and on the final properties of the latex. To investigate particle nucleation mechanisms in emulsion polymerization it is necessary to establish the initial conditions of the emulsified system before the reaction takes place. This research reports on a technique to continuously monitor the droplet size distribution of liquid-liquid emulsions using spectroscopy. The on-line particle characterization methodology is based on an integrated sampling and dilution strategy combined with spectroscopy methods. It is shown that the sampling system integrated with a multiwavelength turbidity detector provides reliable estimates of droplet populations as function of the dispersed phase concentration in emulsions of saturated hydrocarbons. The results provide not only the groundwork necessary for the elucidation of particle nucleation during emulsion polymerization process but also suggests the potential of this combined technology to further our understanding of liquid-liquid emulsions.     

Determination of UV filters in river water samples by in‐line SPE‐CE‐MS

The use of SPE coupled in‐line to CE using electrospray MS detection (in‐line SPE‐CE‐ESI‐MS) was investigated for the preconcentration and separation of four UV filters: benzophenone‐3, 2,2‐dihydroxy‐4‐methoxybenzophenone, 2,4‐dihydroxybenzophenone and 2‐phenylbenzimidazole‐5‐sulphonic acid. First, a CE‐ESI‐MS method was developed and validated using standard samples, obtaining LODs between 0.06 μg/mL and 0.40 μg/mL. For the in‐line SPE‐CE‐ESI‐MS method, three different sorbents were evaluated and compared: Oasis HLB, Oasis MCX, and Oasis MAX. For each sorbent, the main parameters affecting the preconcentration performance, such as sample pH, volume, and composition of the elution plug, and sample injection time were studied. The Oasis MCX sorbent showed the best performance and was used to validate the in‐line SPE‐CE‐ESI‐MS methodology. The LODs reached for standard samples were in the range between 0.01 and 0.05 ng/mL with good reproducibility and the developed strategy provided sensitivity enhancement factors between 3400‐fold and 34 000‐fold. The applicability of the developed methodology was demonstrated by the analysis of UV filters in river water samples.     

基于支座反力影响线曲率差分的等截面连续梁损伤识别方法

为了实现仅采用损伤状态信息对等截面连续梁进行损伤识别,通过推导三跨不等跨连续梁在移动荷载作用下的支座反力影响线,发现支座反力影响线求曲率并作差分后的曲线在损伤位置会发生突变,基于该现象提出了一种损伤定位方法,进一步建立了损伤程度计算方法,可对损伤程度进行较精确的定量。通过一三跨连续梁和一四跨连续梁工程实例的仿真分析,证明了支座反力影响线曲率差分指标损伤定位和相应的损伤程度定量方法对等截面连续梁损伤识别具有可行性。     

滚子摩擦副弹流润滑特性及其应用──Ⅰ 有限长直母线滚子的弹流数值解

运用改进的数值方法求得了与实验结果相符的等温有限长直母线滚子的弹流数值解，与无限长线接触弹流结果相比较，揭示了润滑状态下滚子摩擦副的边缘效应和端泄对油膜分布的影响，在低速和重载时滚子的两端都几乎不能形成全膜润滑，因而有必要通过修形消除滚子端部的边缘效应．     

Existence of frequency modes coupling seismic waves and vibrating tall buildings

We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti-plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet conditions at the interface satisfies a specific integral equation at the base of an idealized tall building. Although numerical simulations suggest that such wavenumbers should exist, as far as we know, to date, there is no theoretical proof of their existence. This is what this present study offers to provide.     

Surface tensor estimation from linear sections

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n‐dimensional Euclidean space. The estimators are based on one‐dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non‐isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.