Electromechanical wave in power systems : theory and applications

The continuum model is a key paradigm describing the behavior of electromechanical transients in power systems. In the past two decades, much research work has been done on applying the continuum model to analyze the electromechanical wave in power systems. In this work, the uniform and non-uniform continuum models are first briefly described, and some explanations borrowing concepts and tools from other fields are given. Then, the existing approaches of investigating the resulting wave equations are summarized. An application named the zero reflection controller based on the idea of the wave equations is next presented.

A comparison of mathematical models for phase separation in high-rate LiFePO4 cathodes

We construct a two-scale mathematical model for modern, high-rate LiFePO4cathodes. We attempt to validate against experimental data using two forms of the phase-field model developed recently to represent the concentration of Li+ in nano-sized LiFePO4crystals. We also compare this with the shrinking-core based model we developed previously. Validating against high-rate experimental data, in which electronic and electrolytic resistances have been reduced is an excellent test of the validity of the crystal-scale model used to represent the phase-change that may occur in LiFePO4material. We obtain poor fits with the shrinking-core based model, even with fitting based on “effective” parameter values. Surprisingly, using the more sophisticated phase-field models on the crystal-scale results in poorer fits, though a significant parameter regime could not be investigated due to numerical difficulties. Separate to the fits obtained, using phase-field based models embedded in a two-scale cathodic model results in “many-particle” effects consistent with those reported recently.

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.

An application of an extended theory of planned behaviour to understand drivers' compliance with the school zones speed limit in Australia and Malaysia

This research investigated individual and situational factors that influence driver compliance with the school zones speed limit in Australia and Malaysia. Despite all the countermeasures implemented in these two countries, driver compliance with the speed limit in school zones is still poor. The findings of the research provided support for the application of the Theory of Planned Behaviour to understand and therefore influence drivers' intention to comply with the school zones speed limit in both Australia and Malaysia. The research also revealed that mindfulness, a construct rarely used in road safety before, directly influenced Australian drivers' intention to comply, while habit influenced intention to comply in Malaysia. The research raised important theoretical and cross-cultural issues for future research and highlighted the need to increase the visibility of school zones with the use of more noticeable traffic control devices.

Directing experience : an exploration of active analysis and visual cognition theory in the training of contemporary directors

The focus of this research is the creation of a stage-directing training manual on the researcher's site at the National Institute of Dramatic Art. The directing procedures build on the work of Stanislavski's Active Analysis and findings from present-day visual cognition studies. Action research methodology and evidence-based data collection are employed to improve the efficacy of both the directing procedures and the pedagogical manual. The manual serves as a supplement to director training and a toolkit for the more experienced practitioner. The manual and research findings provide a unique and innovative contribution to the field of theatre directing.

Combining expert opinions in prior elicitation

We consider the problem of combining opinions from different experts in an explicitly model-based way to construct a valid subjective prior in a Bayesian statistical approach. We propose a generic approach by considering a hierarchical model accounting for various sources of variation as well as accounting for potential dependence between experts. We apply this approach to two problems. The first problem deals with a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. Two hierarchical levels of variation are considered (between and within experts) with a complex mathematical situation due to the use of an indirect probit regression. The second concerns the time taken by PhD students to submit their thesis in a particular school. It illustrates a complex situation where three hierarchical levels of variation are modelled but with a simpler underlying probability distribution (log-Normal).

Universal codes from switching strategies

We discuss algorithms for combining sequential prediction strategies, a task which can be viewed as a natural generalisation of the concept of universal coding. We describe a graphical language based on Hidden Markov Models for defining prediction strategies, and we provide both existing and new models as examples. The models include efficient, parameterless models for switching between the input strategies over time, including a model for the case where switches tend to occur in clusters, and finally a new model for the scenario where the prediction strategies have a known relationship, and where jumps are typically between strongly related ones. This last model is relevant for coding time series data where parameter drift is expected. As theoretical contributions we introduce an interpolation construction that is useful in the development and analysis of new algorithms, and we establish a new sophisticated lemma for analysing the individual sequence regret of parameterised models.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

Spreadsheet Conditional Formatting Illuminates Investigations into Modular Arithmetic

Modular arithmetic has often been regarded as something of a mathematical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digital security systems such as RSA, this important branch of mathematics is now considered essential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Approximate solutions to stochastic dynamic programs

This paper examines the properties of various approximation methods for solving stochastic dynamic programs in structural estimation problems. The problem addressed is evaluating the expected value of the maximum of available choices. The paper shows that approximating this by the maximum of expected values frequently has poor properties. It also shows that choosing a convenient distributional assumptions for the errors and then solving exactly conditional on the distributional assumption leads to small approximation errors even if the distribution is misspecified. © 1997 Cambridge University Press.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.