Modelling the diffuse fraction of global solar radiation on a horizontal surface

For various applications it is necessary to know not only global solar radiation values, but also the diffuse and beam components. Because often only global values are available, there have been several models developed to establish correlations between the diffuse fraction and various predictors. These typically include the clearness index, but also may include the solar angle, temperature and humidity. The clearness index is the proportion of extraterrestrial radiation reaching a location, where the extraterrestrial value used in the calculation varies with latitude and time of year. These correlations have been developed using data principally from latitudes greater than 40°, often using only data from a few locations and with few exceptions have not used solar altitude as a predictor. Generally the data consist of hourly integrated values. A model has been developed using hourly data from a weather station set up at Deakin University, Geelong. Another model has also been developed for 15 minute data values in order to ascertain if the smoothing generated by using hourly data makes a significant difference to overall results. The construction of such models has been investigated, enabling an extension to the research, inclusive of other stations, to be performed systematically. A final investigation was carried out, using data from other Australian locations, to explain some of the considerable scatter by adding apparent solar time as a predictor, which proved to be significantly better than solar altitude.

Advanced modelling of forming high strength steels

The thesis presents a novel approach in the multiscale modelling of Advanced High Strength Steels for prediction of the microstructural effects in forming processes. The results are compared with that of experiments and finite element method. The method is proved to be suitable for complexities in the multiphase AHSS.

Modelling the cooling of coffee : insights from a preliminary study in Indonesia

This paper discusses an attempt to examine pre-service teachers’ mathematical modelling skills. A modelling project investigating relationships between temperature and time in the process of cooling of coffee was chosen. The analysis was based on group written reports of the cooling of coffee project and observation of classroom discussion. Findings showed that pre-service teachers were able to model the process of cooling of coffee as a decreasing exponential function. Difficulties with interpretation of the constant rate of cooling and reinterpretation of mathematical model were identified.

Towards mathematical literacy in the 21st century : perspectives from Indonesia

The notion of mathematical literacy advocated by PISA (OECD, 2006) offers a broader conception for assessing mathematical competences and processes with the main focus on the relevant use of mathematics in life. This notion of mathematical literacy is closely connected to the notion of mathematical modelling whereby mathematics is put to solving real world problems. Indonesia has participated as a partner country in PISA since 2000. The PISA trends in mathematics from 2003 to 2009 revealed unsatisfactory mathematical literacy among 15-year-old students from Indonesia who lagged behind the average of OCED countries. In this paper, exemplary cases will be discussed to examine and promote mathematical literacy at teacher education level. Lesson ideas and instruments were adapted from PISA 2006 released items. The potential of such tasks will be discussed based on case studies of implementing these instruments with samples of pre-service teachers in Yogyakarta. 

Predicting future intensive care demand in Australia

BACKGROUND: Predicting future demand for intensive care is vital to planning the allocation of resources.

METHOD: Mathematical modelling using the autoregressive integrated moving average (ARIMA) was applied to intensive care data from the Australian and New Zealand Intensive Care Society (ANZICS) Core Database and population projections from the Australian Bureau of Statistics to forecast future demand in Australian intensive care.

RESULTS: The model forecasts an increase in ICU demand of over 50% by 2020, with current total ICU bed-days (in 2007) of 471 358, predicted to increase to 643 160 by 2020. An increased rate of ICU use by patients older than 80 years was also noted, with the average bed-days per 10 000 population for this group increasing from 396 in 2006 to 741 in 2007.

CONCLUSION: An increase in demand of the forecast magnitude could not be accommodated within current ICU capacity. Significant action will be required.

Planar waveguide refractive index profile reconstruction using global optimization

The approach taken here of reconstruction of the refractive index profile of planar waveguides involves solving a non-linear integral equation with Tikhonov regularization. Using global optimization with the new cutting angle and discrete gradient methods has yielded an acceptable reconstruction, even in the presence of significant noise in the data.

Joining magnesia partially stabilised zirconia with nickel by current enhancement

This study confirms that current enhancement is a reliable and efficient method for joining ceramic and metal. Experiments indicated very high bond strengths. Mathematical modelling explained the mechanism of joining and has established critical functions for design and control.

An agent-based approach to value theory and wealth distribution in economics

Any attempt to model an economy requires foundational assumptions about the relations between prices, values and the distribution of wealth. These assumptions exert a profound influence over the results of any model. Unfortunately, there are few areas in economics as vexed as the theory of value. I argue in this paper that the fundamental problem with past theories of value is that it is simply not possible to model the determination of value, the formation of prices and the distribution of income in a real economy with analytic mathematical models. All such attempts leave out crucial processes or make unrealistic assumptions which significantly affect the results. There have been two primary approaches to the theory of value. The first, associated with classical economists such as Ricardo and Marx were substance theories of value, which view value as a substance inherent in an object and which is conserved in exchange. For Marxists, the value of a commodity derives solely from the value of the labour power used to produce it - and therefore any profit is due to the exploitation of the workers. The labour theory of value has been discredited because of its assumption that labour was the only ‘factor’ that contributed to the creation of value, and because of its fundamentally circular argument. Neoclassical theorists argued that price was identical with value and was determined purely by the interaction of supply and demand. Value then, was completely subjective. Returns to labour (wages) and capital (profits) were determined solely by their marginal contribution to production, so that each factor received its just reward by definition. Problems with the neoclassical approach include assumptions concerning representative agents, perfect competition, perfect and costless information and contract enforcement, complete markets for credit and risk, aggregate production functions and infinite, smooth substitution between factors, distribution according to marginal products, firms always on the production possibility frontier and firms’ pricing decisions, ignoring money and credit, and perfectly rational agents with infinite computational capacity. Two critical areas include firstly, the underappreciated Sonnenschein-Mantel- Debreu results which showed that the foundational assumptions of the Walrasian general-equilibrium model imply arbitrary excess demand functions and therefore arbitrary equilibrium price sets. Secondly, in real economies, there is no equilibrium, only continuous change. Equilibrium is never reached because of constant changes in preferences and tastes; technological and organisational innovations; discoveries of new resources and new markets; inaccurate and evolving expectations of businesses, consumers, governments and speculators; changing demand for credit; the entry and exit of firms; the birth, learning, and death of citizens; changes in laws and government policies; imperfect information; generalized increasing returns to scale; random acts of impulse; weather and climate events; changes in disease patterns, and so on. The problem is not the use of mathematical modelling, but the kind of mathematical modelling used. Agent-based models (ABMs), objectoriented programming and greatly increased computer power however, are opening up a new frontier. Here a dynamic bargaining ABM is outlined as a basis for an alternative theory of value. A large but finite number of heterogeneous commodities and agents with differing degrees of market power are set in a spatial network. Returns to buyers and sellers are decided at each step in the value chain, and in each factor market, through the process of bargaining. Market power and its potential abuse against the poor and vulnerable are fundamental to how the bargaining dynamics play out. Ethics therefore lie at the very heart of economic analysis, the determination of prices and the distribution of wealth. The neoclassicals are right then that price is the enumeration of value at a particular time and place, but wrong to downplay the critical roles of bargaining, power and ethics in determining those same prices.

Do toddlers need iron-fortified toddler foods to ensure their dietary iron requirements are met?

Adequate nutrition during toddlerhood is essential for optimal growth and development, yet biochemical data suggest that 12-24-month-old children are at risk of iron deficiency. Mathematical modelling combined with experimental interventions can provide strong evidence regarding the types of foods required to improve toddler iron status.

Activating teacher critical moments of learning through reflection

Mathematical modelling is one of the current focuses in the Singapore Mathematics Curriculum Framework. A multi-tiered teaching experiment using design research methodology was conducted to build teachers’ capacity in designing, facilitating, and evaluating learning during mathematical modelling tasks for Primary 5 students (aged 10-11). This paper illustrates the use of the retrospective analysis phase within design research cycles to activate a critical moment of teacher learning involving the interplay between questioning and listening during her first attempt at facilitating a mathematical modelling task. The teacher affirmed her deliberate focuses in the use of questions to (a) refine students’ models, (b) encourage articulation of student ideas in self-evaluation of the models, and (c) clarify and understand student reasoning. However, she also discovered the importance of interpretative listening in conjunction with questioning to promote more sophisticated mathematisation processes in model development. Implications from the use of the retrospective analysis phase on activating critical moments of learning during teacher education will be discussed.

Exemplifying a model-eliciting task for primary school pupils

Mathematical modelling is a field that is gaining prominence recently in mathematics educaiton research and has generated interests in schools as well.  In Singapore, modelling and applications are included as process componens in revised 2007 curriculum document (MOE, 2007) as keeping to reform efforst. In Indonesia, efforts to place stronger emphasis on connecting school mathematics with real-world contexts and applications have started in Indonesian primary schools with the Pendidikan Matematika Realistik Indonesia (PMRI) movement a decade ago (Sembiring, Hoogland, Dolk, 2010). Amidst others, modeling activities are gradually introduced in Singapore and Indonesian schools to demonstrte the relevance of school mathematics with real-world problems. However, on order for it to find a place in the mathematics classroom, ther eis a need for teacher-practitioners to know what mathematical modelling and what a modelling task is. This paper sets out to exemplify a model-eliciting task that has been designed and used in both a Singapore and Indonesian mathematics classroom. Mathematical modelling, the features of a model-eliciting task, and its potential and advice on implementation are discussed. 

Effect of Zn concentration and grain size on prismatic slip in Mg-Zn binary alloys

Mg-Zn binary alloys with concentrations between 0 and 2.8wt% Zn have been prepared and processed via hot rolling and annealing to produce specimens with a strong basal texture and a range of grain sizes. These have been deformed in tension, a condition in which the deformation is dominated by prismatic slip. This data has been used to assess the Hall-Petch parameter as a function of Zn concentration for deformation dominated by prismatic slip. Pure magnesium showed non-linear Hall-Petch behaviour at large grain sizes, and this is compared to the values for prismatic slip measured on single crystals. The differences between critical resolved shear stress measurements made through single crystal, polycrystal and mathematical modelling techniques are also discussed.

Voltage profile improvement for distributed wind generation using D-STATCOM

This paper presents the application of FACTS devices for the enhancement of dynamic voltage stability in distribution networks with distributed wind generation. The analysis is carried over a test distribution system representative of the Kumamoto area in Japan. The detailed mathematical modelling of the system is also presented. Firstly, this paper provides simulation results showing the effects of higher and lower penetration of distributed wind generation on the voltage dynamics in a faulted system. Then, a distribution static synchronous compensator (D-STATCOM) is used to improve the voltage profile of the system. This analysis shows that D-STATCOM has significant performance to improve the voltage dynamics of distribution system compared to shunt capacitor.