A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

Examining the influence of participant performance factors on contractor satisfaction : a structural equation model

Participant performance is critical to the success of projects. At the same time, enhancing the satisfaction of participants not only helps in problem solving but also improves their motivation and cooperation. However, previous research related to participant satisfaction is primarily concerned with clients and customers and relatively little attention has been paid to contractors. This paper investigates how the performance of project participants affects contractor project satisfaction in terms of the client's clarity of objectives (OC) and promptness of payments (PP), designer carefulness (DC), construction risk management (RM), the effectiveness their contribution (EW) and mutual respect and trust (RT). With 125 valid responses from contractors in Malaysia, a contractor satisfaction model is developed based on structural equation modelling. The results demonstrate the necessity for dividing abstract satisfaction into two dimensions, comprising economic-related satisfaction (ES) and production-related satisfaction (PS), with DC, OC, PP and RM having significant effects on ES, while DC, OC, EW and RM influence PS. In addition, the model tests the indirect effects of these performance variables on ES and PS. In particular, OC indirectly affects ES and PS through mediation of RM and DC respectively. The results also provide opportunities for improving contractor satisfaction and supplementing the contractor selection criteria for clients.

Constitutive production of IL-13 promotes early-life Chlamydia respiratory infection and allergic airway disease

Deleterious responses to pathogens during infancy may contribute to infection and associated asthma. Chlamydia respiratory infections in early life are common causes of pneumonia and lead to reduced lung function and asthma. We investigated the role of interleukin-13 (IL-13) in promoting early-life Chlamydia respiratory infection, infection-induced airway hyperresponsiveness (AHR), and severe allergic airway disease (AAD). Infected infant Il13−/− mice had reduced infection, inflammation, and mucus-secreting cell hyperplasia. Surprisingly, infection of wild-type (WT) mice did not increase IL-13 production but reduced IL-13Rα2 decoy receptor levels compared with sham-inoculated controls. Infection of WT but not Il13−/− mice induced persistent AHR. Infection and associated pathology were restored in infected Il13−/− mice by reconstitution with IL-13. Stat6−/− mice were also largely protected. Neutralization of IL-13 during infection prevented subsequent infection-induced severe AAD. Thus, early-life Chlamydia respiratory infection reduces IL-13Rα2 production, which may enhance the effects of constitutive IL-13 and promote more severe infection, persistent AHR, and AAD.

Heritage language for Chinese Australians : negotiating 'Chineseness' and, capitalising on resources in the lived world

The ethnic identity and commitment of Heritage Language Learners play salient roles in Heritage Language learning process. The mutually constitutive effect amongst Heritage Language Learner's ethnic identity, commitment, and Heritage Language proficiency has been well documented in social psychological and poststructuralist literatures. Both social psychological and poststructural schools offer meaningful insights into particular contexts but receive critiques from other contexts. In addition, the two schools largely oppose each other. This study uses Bourdieu's sociological triad of habitus, capital, and field to reconcile the two schools through the examination of Chinese Heritage Language Learners in Australia, an idiosyncratic social, cultural, and historical context for these learners. Specifically, this study investigates how young Chinese Australian adults (18-35 in age) negotiate their 'Chineseness' and capitalise on resources through Chinese Heritage Language learning in the lived world. The study adopts an explanatory mixed methods design to combine the quantitative approach with the qualitative approach. The initial quantitative phase addresses the first research question: Is Chinese Heritage Language proficiency of young Chinese Australian adults influenced by their investment of capital, the strength of their habitus of 'Chineseness', or both? The subsequent qualitative phase addresses the second research question: How do young Chinese Australian adults understand their Chinese Heritage Language learning in relation to (potential) profits produced by this linguistic capital in given fields? The initial quantitative phase applies Structural Equation Modelling to analyse the data from an online survey with 230 respondents. Findings indicate the statistically significant positive contribution made by the habitus of 'Chineseness' and by investment of capital to Chinese Heritage Language proficiency (r = .71 and r = .86 respectively). Subsequent multiple regression analysis demonstrates that 62% of the variance of Chinese Heritage Language proficiency can be accounted for by the joint contribution of 'Chineseness' and 'capital'. The qualitative phase of the study uses multiple interviews with five participants. It reveals that Chinese Heritage Language offers meaningful benefits for participants in the forms of capital production and habitus capture or recapture. Findings from the two phases talk to each other in terms of the inherent entanglement amongst habitus of 'Chineseness', investment of capital, and Chinese Heritage Language proficiency. The study offers important contributions. Theoretically, by virtue of Bourdieu's signature concepts of habitus, capital, and field, the study provides answers to questions that both social psychological and poststructuralist theories have long been struggling to answer. Methodologically, the position of 'pluralism' talks back to Bourdieu's theory and forwards to the mixed methods design. Particularly, the study makes a methodological breakthrough: A set of instruments was developed and validated to quantify Bourdieu's key concepts of capital and habitus within certain social fields. Practically, understanding Chinese Australians' heterogeneity and the potential drivers behind Chinese Heritage Language learning contributes to the growing interest in Chinese Australians' contemporary life experiences and helps to better accommodate linguistically diverse Chinese Heritage Language Learners in Chinese language courses. In addition, this study is very timely. It resonates with the recently released Australia in the Asian Century White Paper: Chinese Australians, with sound knowledge of Chinese culture and language obtained through negotiating their 'Chineseness' and capitalising on diverse resources for learning, will help to serve Australia's economic, social, and political needs in unique ways.

Hyperelastic constitutive relationship for the strain-rate dependent behavior of shoulder and other joint cartilages

Non-linear finite deformations of articular cartilages under physiological loading conditions can be attributed to hyperelastic behavior. This paper contains experimental results of indentation tests in finite deformation and proposes an empirical based new generalized hyperelastic constitutive model to account for strain-rate dependency for humeral head cartilage tissues. The generalized model is based on existing hyperelastic constitutive relationships that are extensively used to represent biological tissues in biomechanical literature. The experimental results were obtained for three loading velocities, corresponding to low (1x10-3 s-1), moderate and high strain-rates (1x10-1 s-1), which represent physiological loading rates that are experienced in daily activities such as lifting, holding objects and sporting activities. Hyperelastic material parameters were identified by non linear curve fitting procedure. Analysis demonstrated that the material behavior of cartilage can be effectively decoupled into strain-rate independent(elastic) and dependent parts. Further, experiments conducted using different indenters indicated that the parameters obtained are significantly affected by the indenter size, potentially due to structural inhomogeneity of the tissue. The hyperelastic constitutive model developed in this paper opens a new avenue for the exploration of material properties of cartilage tissues.

Nedd4-2functionally interacts with ClC-5: involvement in constitutive albumin endocytosis in proximal tubule cells

Constitutive albumin uptake by the proximal tubule is achieved by a receptor-mediated process in which the Cl– channel, ClC-5, plays an obligate role. Here we investigated the functional interaction between ClC-5 and ubiquitin ligases Nedd4 and Nedd4-2 and their role in albumin uptake in opossum kidney proximal tubule (OK) cells. In vivo immunoprecipitation using an anti-HECT antibody demonstrated that ClC-5 bound to ubiquitin ligases, whereas glutathione S-transferase pull-downs confirmed that the C terminus of ClC-5 bound both Nedd4 and Nedd4-2. Nedd4-2 alone was able to alter ClC-5 currents in Xenopus oocytes by decreasing cell surface expression of ClC-5. In OK cells, a physiological concentration of albumin (10 μg/ml) rapidly increased cell surface expression of ClC-5, which was also accompanied by the ubiquitination of ClC-5. Albumin uptake was reduced by inhibiting either the lysosome or proteasome. Total levels of Nedd4-2 and proteasome activity also increased rapidly in response to albumin. Overexpression of ligase defective Nedd4-2 or knockdown of endogenous Nedd4-2 with small interfering RNA resulted in significant decreases in albumin uptake. In contrast, pathophysiological concentrations of albumin (100 and 1000 μg/ml) reduced the levels of ClC-5 and Nedd4-2 and the activity of the proteasome to the levels seen in the absence of albumin. These data demonstrate that normal constitutive uptake of albumin by the proximal tubule requires Nedd4-2, which may act via ubiquitination to shunt ClC-5 into the endocytic pathway.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

A derivation of high-frequency asymptotic values of 3D added mass and damping based on properties of the Cummins' equation

This brief paper provides a novel derivation of the known asymptotic values of three-dimensional (3D) added mass and damping of marine structures in waves. The derivation is based on the properties of the convolution terms in the Cummins's Equation as derived by Ogilvie. The new derivation is simple and no approximations or series expansions are made. The results follow directly from the relative degree and low-frequency asymptotic properties of the rational representation of the convolution terms in the frequency domain. As an application, the extrapolation of damping values at high frequencies for the computation of retardation functions is also discussed.

Predicting emotional exhaustion among haemodialysis nurses : a structural equation model using Kanter’s structural empowerment theory

Aim To test an explanatory model of the relationships between the nursing work environment, job satisfaction, job stress and emotional exhaustion for haemodialysis nurses, drawing on Kanter's theory of organizational empowerment. Background Understanding the organizational predictors of burnout (emotional exhaustion) in haemodialysis nurses is critical for staff retention and improving nurse and patient outcomes. Previous research has demonstrated high levels of emotional exhaustion among haemodialysis nurses, yet the relationships between nurses' work environment, job satisfaction, stress and emotional exhaustion in this population are poorly understood. Design A cross-sectional online survey. Methods 417 nurses working in haemodialysis units completed an online survey between October 2011–April 2012 using validated measures of the work environment, job satisfaction, job stress and emotional exhaustion. Results Overall, the structural equation model demonstrated adequate fit and we found partial support for the hypothesized relationships. Nurses' work environment had a direct positive effect on job satisfaction, explaining 88% of the variance. Greater job satisfaction, in turn, predicted lower job stress, explaining 82% of the variance. Job satisfaction also had an indirect effect on emotional exhaustion by mitigating job stress. However, job satisfaction did not have a direct effect on emotional exhaustion. Conclusion The work environment of haemodialysis nurses is pivotal to the development of job satisfaction. Nurses' job satisfaction also predicts their level of job stress and emotional exhaustion. Our findings suggest staff retention can be improved by creating empowering work environments that promote job satisfaction among haemodialysis nurses.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.