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.

Developing a framework for work integrated research higher degree studies in an Australian engineering context

The umbrella of Australian research higher degree (RHD) offerings has broadened from the traditional MPhil/PhD programmes to include a range of professional masters and doctoral degrees. This article reports on the experiences of three PhD students, engaged in an informally managed industry partnered research programme, described in this article as the work integrated research higher degree (WIRHD). Their learning process shares the attributes from both the traditional PhD programme and professional doctorates. However, because of the blended nature of the learning contexts, candidates engaged in the WIRHD programme must address a wider range of issues than those following the traditional RHD pathway. An exploratory case study approach was adopted with the view to develop an integrative framework to explain the various contexts that influence the learning experience of WIRHD candidates, as well as a structured approach to guide this contemporary form of industry partnered WIRHD process.

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.

Higher degree research at Australian Universities : Responding to diversity in engineering and information technology

BACKGROUND There is increasing enrolment of international students in the Engineering and Information Technology disciplines and anecdotal evidence of a need for additional understanding and support for these students and their supervisors due to differences both in academic and social cultures. While there is a growing literature on supervisory styles and guidelines on effective supervision, there is little on discipline-specific, cross-cultural supervision responding to the growing diversity. In this paper, we report findings from a study of Engineering and Information technology Higher Degree Research (HDR)students and supervision in three Australian universities. PURPOSE The aim was to assess perceptions of students and supervisors of factors influencing success that are particular to international or culturally and linguistically diverse (CaLD) HDR students in Engineering and Information technology. DESIGN/METHOD Online survey and qualitative data was collected from international and CaLD HDR students and supervisors at the three universities. Bayesian network analysis, inferential statistics, and qualitative analysis provided the main findings. RESULTS Survey results indicate that both students and supervisors are positive about their experiences, and do not see language or culture as particularly problematic. The survey results also reveal strong consistency between the perceptions of students and supervisors on most factors influencing success. Qualitative analysis of critical supervision incidents has provided rich data that could help improve support services. CONCLUSIONS In contrast with anecdotal evidence, HDR completion data from the three universities reveal that international students, on average, complete in shorter time periods than domestic students. The analysis suggests that success is linked to a complex set of factors involving the student, supervision, the institution and broader community.

Work integrated research higher degree studies : experiences, benefits, barriers and coping strategies

Attributed to the changing social, political and economic landscape of the ‘knowledge economy’, Australian universities are under pressure to produce researchers that have a variety of skills which meet the demands of an increasingly diverse job market. As a consequence, the Australian PhD now includes a range of doctoral degrees. This paper reports on the experiences of two PhD students engaged in an informally managed research higher degree program described in this paper as a Work Integrated Research Higher Degree (WIRHD). Their learning process shares the attributes from both the traditional PhD program and professional doctorates. However, because of the blended nature of the learning contexts, what students need to manage within the WIRHD is much more complicated than the established RHD programs. An exploratory case study approach exploring experiences, benefits, barriers and coping strategies was conducted with the view to develop a preliminary integrative framework that attempts to explain the various contexts that influence the learning experience of WIRHD candidates. The paper concludes with some recommended strategies for helping WIRHD candidates to manage the challenges associated with their learning process.

Cooking enhances but the degree of ripeness does not affect provitamin A carotenoid bioavailability from bananas

Banana is a staple crop in many regions where vitamin A deficiency is prevalent, making it a target for provitamin A biofortification. However, matrix effects may limit provitamin A bioavailability from bananas. The retinol bioefficacies of unripe and ripe bananas (study 1A), unripe high-provitamin A bananas (study 1B), and raw and cooked bananas (study 2) were determined in retinol-depleted Mongolian gerbils (n = 97/study) using positive and negative controls. After feeding a retinol-deficient diet for 6 and 4 wk in studies 1 and 2, respectively, customized diets containing 60, 30, or 15% banana were fed for 17 and 13 d, respectively. In study 1A, the hepatic retinol of the 60% ripe Cavendish group (0.52 ± 0.13 μmol retinol/liver) differed from baseline (0.65 ± 0.15 μmol retinol/liver) and was higher than the negative control group (0.39 ± 0.16 μmol retinol/liver; P < 0.0065). In study 1B, no groups differed from baseline (0.65 ± 0.15 μmol retinol/liver; P = 0.20). In study 2, the 60% raw Butobe group (0.68 ± 0.17 μmol retinol/liver) differed from the 60% cooked Butobe group (0.87 ± 0.24 μmol retinol/liver); neither group differed from baseline (0.80 ± 0.27 μmol retinol/liver; P < 0.0001). Total liver retinol was higher in the groups fed cooked bananas than in those fed raw (P = 0.0027). Body weights did not differ even though gerbils ate more green, ripe, and raw bananas than cooked, suggesting a greater indigestible component. In conclusion, thermal processing, but not ripening, improves the retinol bioefficacy of bananas. Food matrix modification affects carotenoid bioavailability from provitamin A biofortification targets.

Effect of environmental conditions on degree of hoof wall hydration in horses

Objective: To determine the effect of various environmental conditions on the degree of hydration in hoof wall horn tissue from feral horses and investigate the effect of short-term foot soaking on moisture content in hoof wall and sole tissue in domestic horses. Animals: 40 feral horses from 3 environments (wet and boggy [n = 10], partially flooded [20], and constantly dry desert [10]) and 6 nonferal Quarter Horses. Procedures: The percentage of moisture content of hoof wall samples from feral horses was measured in vitro. In a separate evaluation, the percentage of moisture content of hoof wall and sole tissue was measured in the dry and soaked forefeet of Quarter Horses. Results: Mean ± SD percentage of moisture content was 29.6 ± 5.1%, 29.5 ± 5.8%, and 29.5 ± 2.9% for feral horses from the wet and boggy, partially flooded, and constantly dry desert environments, respectively. Moisture content did not differ among the 3 groups, nor did it differ between dry and soaked hoof wall samples from nonferal horses. However, soaking in water for 2 hours resulted in a significant increase in the percentage of moisture content of the sole. Conclusions and Clinical Relevance: Environmental conditions do not appear to affect moisture content in the hoof wall horn. Soaking horses' feet regularly in water would be unlikely to change the degree of hydration in the hoof wall horn but may further hydrate the sole.

Heuristics and building price forecasting

The construction industry contains two types of estimators the contractors' estimator and the designers' price forecaster. Each has two models of the building in which to systemize his procedures - the production model and the design model. The use of these models is discussed in the light of the industry's particular problems of complexity and uncertainty together with the pressures of the market. It is argued that estimators and forecasters, in order to function effectively in these conditions, are forced to exercise a high degree of subjective judgment. Means of eliciting good heuristics involved in judgment making are considered by reference to the artificial intelligence and construction literature and a methodology is proposed based on these findings. The results of two early trials of the method with students are given, indicating the usefulness of the approach.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

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.