Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.

Secure Implementation in Production Economies

This paper shows that, in production economies, the generalized serial social choice functions defined by Shenker (1992) are securely implementable (in the sense of Saijo et al., 2007) and that they include the well-known fixed path social choice functions.

Derivation of scientific software from mathematical specifications

Often the modification and enhancement of large scientific software systems are severely hampered because many components of the system are written in an implementation dependent fashion, they are inadequately documented, and their functionalities are not precisely known. In this paper we consider how mathematics may be employed to alleviate some of these problems. In particular, we illustrate how the formal specification notation VDM-SL is being used to specify precisely abstract data types for use in the development of scientific software.

Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

Mathematics and reading difficulty subtypes: Minor phonological influences on mathematics for 5-7 year olds

Linguistic influences in mathematics have previously been explored throughsubtyping methodology and by taking advantage of the componential nature ofmathematics and variations in language requirements that exist across tasks. Thepresent longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5-7 years. Initially, 256 children were screened for mathematics and reading difficulties using standardised measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the MD (n=26), MDRD (n=32), reading difficulty (RD, n=22) and typically achieving (TA, n=35) subtypes. These children were tested at four time points, separated by six monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypescould have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.

Mathematical modelling of quantum yield enhancements of methyl orange photooxidation in aqueous TiO2 suspensions under controlled periodic UV LED illumination

Quantum yields of the photocatalytic degradation of methyl orange under controlled periodic illumination (CPI) have been modelled using existing models. A modified Langmuir-Hinshelwood (L-H) rate equation was used to predict the degradation reaction rates of methyl orange at various duty cycles and a simple photocatalytic model was applied in modelling quantum yield enhancement of the photocatalytic process due to the CPI effect. A good agreement between the modelled and experimental data was observed for quantum yield modelling. The modified L-H model, however, did not accurately predict the photocatalytic decomposition of the dye under periodic illumination.