The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Practice and Procedure: UCPR r 708 - costs order against several defendants and third party

Glenwood Homes Pty Ltd v Everhard [2008] QSC 192 involved the not uncommon situation where one costs order is made against several parties represented by a single firm of solicitors. Dutney J considered the implications when only some of the parties liable for the payment of the costs file a notice of objection to the costs statement served in respect of those costs.

Family violence or woman abuse? Putting gender back into the Canadian research equation

Research on violence against women has been among the most scrutinized areas in social science. From the beginning, efforts to empirically document the prevalence, incidence, and characteristics of violence against women have been hotly debated (DeKeseredy, 2011; Dragiewicz & DeKeseredy, forthcoming; Minaker & Snider, 2006). Objections that violence against women was rare have given way to acknowledgement that it is more common than once thought. Research on the outcomes of woman abuse has documented the serious ramifications of this type of violence for individual victims and the broader community. However, violence against women was not simply “discovered” by scholars in the 1960s, leading to a progressive growth of the literature. Knowledge production around violence against women has been fiercely contested, and feminist insights in particular have always been met with backlash(Gotell, 2007; Minkaer & Snider, 2006; Randall, 1989; Sinclair, 2003)...

Federal Court Rules O23 r 11 - offers of compromise - offer for dismissal of claim and to forego recovery of costs.

In Uniline Australia Ltd ACN 010752057 v S Briggs Pty Ltd ACN 007415518 (No 2) [2009] FCA 920 Greenwood J considered a number of principles guiding the exercise of discretion in relation to costs, particularly when offers of compromise have been made under the formal process provided by the Federal Court Rules.

A sociological quantitative study about Chineseness and Chinese heritage language for young Chinese Australian adults in urban Australia

The relationship between Heritage Language and ethnic identity has gained significant research ground in North America. However, there is a dearth of similar research conducted in other regions of the world. There seems to be little if any work investigating the link between Chinese Australians’ ethnic identity and their Chinese Heritage Language. This sociological quantitative study interpreted Chinese Australians’ “Chineseness” as their ethnic identity, linked this “Chineseness” to their Chinese Heritage Language, and did so by virtue of Bourdieu’s key concept ‘habitus’. 227 cases were analyzed by Structural Equation Modelling. The result demonstrated a statistically significant strong positive relationship between Chinese Australian urban young adults’ “Chineseness” and their self-perceptions of their Chinese Heritage Language proficiency (r=.73). This paper explained the findings in light of Bourdieu’s (1991) contention that people make choices about languages according to the habitus they have.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Reliable and valid survey design for structural equation modelling

My quantitative study asks how Chinese Australians’ “Chineseness” and their various resources influence their Chinese language proficiency, using online survey and snowball sampling. ‘Operationalization’ is a challenging process which ensures that the survey design talks back to the informing theory and forwards to the analysis model. It requires the attention to two core methodological concerns, namely ‘validity’ and ‘reliability’. Construction of a high-quality questionnaire is critical to the achievement of valid and reliable operationalization. A series of strategies were chosen to ensure the quality of the questions, and thus the eventual data. These strategies enable the use of structural equation modelling to examine how well the data fits the theoretical framework, which was constructed in light of Bourdieu’s theory of habitus, capital and field.

RcppArmadillo : accelerating R with high-performance C++ linear algebra

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to high-performance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

Brokering innovation to better leverage R&D investment

What is the contribution of innovation brokers in leveraging research and development (R&D) investment to enhance industry-wide capabilities? The case of the Australian Cooperative Research Centre for Construction Innovation (CRC CI) is considered in the context of motivating supply chain firms to improve their organizational capabilities in order to acquire, assimilate, transfer and exploit R&D outcomes to their advantage, and to create broader industry and national benefits. A previous audit and analysis has shown an increase in business R&D investment since 2001. The role of the CRC CI in contributing to growth in the absorptive capacity of the Australian construction industry as a whole is illustrated through two programmes: digital modelling building information modelling (BIM) and construction site safety. Numerous positive outcomes in productivity, quality, improved safety and competitiveness were achieved between 2001 and 2009.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.