A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Series in vector spherical harmonics : an efficient tool for solution of nonlinear problems in spherical plasmas

The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

Using enterprise information architecture methods to model wicked problems in information systems design research

Design Science is the process of solving ‘wicked problems’ through designing, developing, instantiating, and evaluating novel solutions (Hevner, March, Park and Ram, 2004). Wicked problems are described as agent finitude in combination with problem complexity and normative constraint (Farrell and Hooker, 2013). In Information Systems Design Science, determining that problems are ‘wicked’ differentiates Design Science research from Solutions Engineering (Winter, 2008) and is a necessary part of proving the relevance to Information Systems Design Science research (Hevner, 2007; Iivari, 2007). Problem complexity is characterised as many problem components with nested, dependent and co-dependent relationships interacting through multiple feedback and feed-forward loops. Farrell and Hooker (2013) specifically state for wicked problems “it will often be impossible to disentangle the consequences of specific actions from those of other co-occurring interactions”. This paper discusses the application of an Enterprise Information Architecture modelling technique to disentangle the wicked problem complexity for one case. It proposes that such a modelling technique can be applied to other wicked problems and can lay the foundations for proving relevancy to DSR, provide solution pathways for artefact development, and aid to substantiate those elements required to produce Design Theory.

Drawing out critical thinking : testing the methodological value of drawing collaboratively

Early childhood research has long established that drawing is a central, and important activity for young children. Less common are investigations into the drawing activity of adults involved in early childhood. A team of adult early childhood researchers, with differing exposures and familiarities with drawing, experimented with intergenerational collaborative drawing with colleagues, students, family members and others, to explore the effectiveness of drawing as a research process and as an arts-based methodology. This testing prompted critical thinking into how drawing might facilitate research that involves young children, to operate in more communicable ways, and how research-focused drawings might occur in reference to a research project.

A robust methodological approach for mine site water accounting

Over the past decade, the mining industry has come to recognise the importance of water both to itself and to others. Water accounting is a formalisation of this importance that quantifies and communicates how water is used by individual sites and the industry as a whole. While there are a number of different accounting frameworks that could be used within the industry, the Minerals Council of Australia’s (MCA) Water Accounting Framework (WAF) is an industry-led approach that provides a consistent representation of mine site water interactions regardless of their operational, social or environmental context that allows for valid comparisons between sites and companies. The WAF contains definitions of offsite water sources and destinations and onsite water use, a methodology for applying the definitions and a set of metrics to measure site performance. The WAF is comprised of two models: the Input-Output Model, which represents the interactions between sites and their surrounding community and the Operational Model, which represents onsite water interactions. Members of the MCA have recently adopted the WAF’s Input-Output Model to report on their external water interactions in their Australian operations with some adopting it on a global basis. To support this adoption, there is a need for companies to better understand how to implement the WAF in their own operations. Developing a water account is non-trivial, particularly for sites unfamiliar with the WAF or for sites with the need to represent unusual features. This work describes how to build a water account for a given site using the Input-Output Model with an emphasis on how to represent challenging situations.

Studying refugee settlement through longitudinal research : methodological and ethical insights from the Good Starts study

Research involving resettled refugees raises methodological and ethical complexities. These complexities typically emerge within cross-sectional research that focuses on refugee experiences at a specific point in time. Given the long term and dynamic nature of refugee settlement, longitudinal research is valuable, yet it raises distinct complexities within the research process. This article focuses on the methodological and ethical insights that emerged in a longitudinal study of settlement and wellbeing with a cohort of young people from refugee backgrounds in Australia. It considers: engagement and retention of a cohort over time; the need to adapt research tools to changing settlement contexts and life stages; participants’ experiences of long-term involvement in the study; and the challenge of timely translation of findings into evidence for policy and practice. The article contributes to a growing understanding of the practical, ethical and epistemological challenges and opportunities presented by longitudinal research, in this case, with resettled refugee background youth.

Wicked problems in designing open online learning

This paper will report on the “wicked” problems encountered when designing an online course with bounded content in an unbounded learning environment. It will describe the dilemmas faced and decisions made by academics in an Australian university challenged by an institutional initiative to design radical, disruptive learning experiences making use of readily available online media. This bounded/unbounded environment demands new roles for instructors in adopting innovative pedagogies and teaching and learning strategies. It also creates changing and challenging roles for course designers as they deal with ill-defined parameters and unknown audiences. In this paper, we propose a novel methodology for making curricular decisions in ill-defined spaces.

Simulation study for analysis of online dielectric measurement problems on transformer insulation system

Determining the condition as well as the remaining life of an insulation system is essential for the reliable operation of large oil-filled power transformers. Frequency-domain spectroscopy (FDS) is one of the diagnostic techniques used to identify the dielectric status of a transformer. Currently, this technique can only be implemented on a de-energized transformer. This paper presents an initial investigation into a novel online monitoring method based on FDS dielectric measurements for transformers. The proposed technique specifically aims to address the real operational constraints of online testing. This is achieved by designing an online testing model extending the basic “extended Debye” linear dielectric model and taking unique noise issues only experienced during online measurements into account via simulations. Approaches to signal denoising and potential problems expected to be encountered during online measurements will also be discussed. Using fixed-frequency sinusoidal excitation waveforms will result in a long measurement times. The use of alternatives such as a chirp has been investigated using simulations. The results presented in the paper predict that reliable measurements should be possible during online testing.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

Expanded review criteria : the case of nonpharmacological interventions in dementia

This paper challenges the assumptions underlying many reviews and offers alternative criteria for examining evidence for nonpharmacological interventions. We evaluated 27 reviews examining interventions for persons with dementia as they relate to the issues of selection based on randomized controlled trial (RCT) design. Reviews were described by type of intervention, level of cognitive function, and criteria for inclusion. Of the 27 reviews, 46% required RCTs for inclusion and most had stringent inclusion criteria. This resulted in poor utilization of the literature and low ecological validity. Eliminating most of the available data poses a critical problem to clinical and research development. Studies meeting strict methodological criteria may not generalize to the greater population or may exclude sub-populations and interventions. Limitations of double-blind RCTs and potential design solutions are set forth based on appropriate populations, problems, interventions, and settings characteristics.