The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Remaining useful life prediction of rotating equipment using covariate-based hazard models : industry applications

The ability to estimate the expected Remaining Useful Life (RUL) is critical to reduce maintenance costs, operational downtime and safety hazards. In most industries, reliability analysis is based on the Reliability Centred Maintenance (RCM) and lifetime distribution models. In these models, the lifetime of an asset is estimated using failure time data; however, statistically sufficient failure time data are often difficult to attain in practice due to the fixed time-based replacement and the small population of identical assets. When condition indicator data are available in addition to failure time data, one of the alternate approaches to the traditional reliability models is the Condition-Based Maintenance (CBM). The covariate-based hazard modelling is one of CBM approaches. There are a number of covariate-based hazard models; however, little study has been conducted to evaluate the performance of these models in asset life prediction using various condition indicators and data availability. This paper reviews two covariate-based hazard models, Proportional Hazard Model (PHM) and Proportional Covariate Model (PCM). To assess these models’ performance, the expected RUL is compared to the actual RUL. Outcomes demonstrate that both models achieve convincingly good results in RUL prediction; however, PCM has smaller absolute prediction error. In addition, PHM shows over-smoothing tendency compared to PCM in sudden changes of condition data. Moreover, the case studies show PCM is not being biased in the case of small sample size.

Discrete families of Saffman–Taylor fingers with exotic shapes

The mathematical problem of determining the shape of a steadily propagating Saffman–Taylor finger in a rectangular Hele-Shaw cell is known to have a countably infinite number of solutions for each fixed surface tension value. For sufficiently large surface tension values, we find that fingers on higher solution branches are non-convex. The tips of the fingers have increasingly exotic shapes as the branch number increases.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

Are there generalizable trends in the release of airborne synthetic clay nanoparticles from a jet milling process?

Despite recent efforts to assess the release of nanoparticles to the workplace during different nanotechnology activities, the existence of a generalizable trend in the particle release has yet to be identified. This study aimed to characterize the release of synthetic clay nanoparticles from a laboratory-based jet milling process by quantifying the variations arising from primary particle size and surface treatment of the material used, as well as the feed rate of the machine. A broad range of materials were used in this study, and the emitted particles mass (PM2.5) and number concentrations (PNC) were measured at the release source. Analysis of variance, followed by linear mixed-effects modeling, was applied to quantify the variations in PM2.5 and PNC of the released particles caused by the abovementioned factors. The results confirmed that using materials of different primary size and surface treatment affects the release of the particles from the same process by causing statistically-significant variations in PM2.5 and PNC. The interaction of these two factors should also be taken into account as it resulted in variations in the measured particles release properties. Furthermore, the feed rate of the milling machine was confirmed to be another influencing parameter. Although this research does not identify a specific pattern in the release of synthetic clay nanoparticles from the jet milling process generalizable to other similar settings, it emphasizes that each tested case should be handled individually in terms of exposure considerations.

Airborne culturable fungi in naturally ventilated primary school environments in a subtropical climate

There is currently a lack of reference values for indoor air fungal concentrations to allow for the interpretation of measurement results in subtropical school settings. Analysis of the results of this work established that, in the majority of properly maintained subtropical school buildings, without any major affecting events such as floods or visible mould or moisture contamination, indoor culturable fungi levels were driven by outdoor concentration. The results also allowed us to benchmark the “baseline range” concentrations for total culturable fungi, Penicillium spp., Cladosporium spp. and Aspergillus spp. in such school settings. The measured concentration of total culturable fungi and three individual fungal genera were estimated using Bayesian hierarchical modelling. Pooling of these estimates provided a predictive distribution for concentrations at an unobserved school. The results indicated that “baseline” indoor concentration levels for indoor total fungi, Penicillium spp., Cladosporium spp. and Aspergillus spp. in such school settings were generally ≤ 1450, ≤ 680, ≤ 480 and ≤ 90 cfu/m3, respectively, and elevated levels would indicate mould damage in building structures. The indoor/outdoor ratio for most classrooms had 95% credible intervals containing 1, indicating that fungi concentrations are generally the same indoors and outdoors at each school. Bayesian fixed effects regression modeling showed that increasing both temperature and humidity resulted in higher levels of fungi concentration.

Inhaled particle surface area dose: Stationary vs personal monitoring

The aim of this paper is to determine the suitability of solely stationary measurements for exposure assessment and management applications. For this purpose, quantified inhaled particle surface area (IPSA) doses using both stationary and personal particle exposure monitors were evaluated and compared.

Characterisation and sources of ultrafine particles in an inner city urban area

Exposure to atmospheric ultrafine particles (UFPs, D<100 nm) has been an increasingly concern because of their potential impact one health. Motor vehicle emissions are considered as one of the major source of UFPin urban airshed, as the combustion of both petrol and diesel engine leads to emission of particles which are predominantly in this size range (Ban-Weiss et al, 2010; Morawska et al, 2008). New particle formations (NPFs) and major facilities such as airport or seaport has also been identified as major sources of UFPs in urban airshed (Cheung et al, 2010; González et al, 2011; Mazaheri et al, 2013). However, contribution of those urban sources to ambient UFP concentrations has not been comprehensively characterized.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

Modelling intermittent microwave convective drying (IMCD) of food materials

This thesis develops comprehensive mathematical models for an advanced drying technology Intermittent Microwave Convective Drying (IMCD). The models provide an improved physical understanding of the heat and mass transport during the drying process, which will help to improve the quality of dried food and energy efficiency of the process, as well as will increase the ability of automation and optimization. The final model in this thesis represents the most comprehensive fundamental multiphase model for IMCD that considers 3D electromagnetics coupled with multiphase porous media transport processes. The 3D electromagnetics considers Maxwell's equation and multiphase transport model considers three different phases: solid matrix, liquid water and gas consisting water vapour and air. The multiphase transport includes pressure-driven flow, capillary diffusion, binary diffusion, and evaporation. The models developed in this thesis were validated with extensive experimental investigations.

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.

New microscale vertically oriented organic photovoltaics cells

We initially look at the changing energy environment and how that can have a dramatic change on the potential of alternative energies, in particular those of organic photovoltaicvs (OPV) cells. In looking at OPV's we also address the aspects of where we are with the current art and why we may not be getting the best from our materials. In doing so, we propose the idea of changing how we build organic photovoltaics by addressing the best method to contain light within the devices. Our initial effort is in addressing how these microscale optical concentrators work in the form of optical fibers in terms of absorption. We have derived a mathematical method which takes account of the input angle of light to achieve optimum absorption. However, in doing so we also address the complex issue how the changing refractive indices in a multilayer device can alter how we input the light. We have found that by knowing the materials refractive index our model takes into account the incident plane, meridonal plane, cross sectional are and path length to ensure optical angular input. Secondly, we also address the practicalities of making such vertical structures the greater issue of changing light intensity incident on a solar cell and how that aspects alters how we view the performance of organic solar cells.

Mathematical models for collective cell spreading

Collective cell spreading is frequently observed in development, tissue repair and disease progression. Mathematical modelling used in conjunction with experimental investigation can provide key insights into the mechanisms driving the spread of cell populations. In this study, we investigated how experimental and modelling frameworks can be used to identify several key features underlying collective cell spreading. In particular, we were able to independently quantify the roles of cell motility and cell proliferation in a spreading cell population, and investigate how these roles are influenced by factors such as the initial cell density, type of cell population and the assay geometry.

Interaction design for tablet based edutainment systems for mathematical education of primary student

Mathematics has been perceived as the core area of learning in most educational systems around the world including Sri Lanka. Unfortunately, it is clearly visible that a majority of Sri Lankan students are failing in their basic mathematics when the recent grade five scholarship examination and ordinary level exam marks are analysed. According to Department of Examinations Sri Lanka , on average, over 88 percent of the students are failing in the grade 5 scholarship examinations where mathematics plays a huge role while about 50 percent of the students fail in there ordinary level mathematics examination. Poor or lack of basic mathematics skills has been identified as the root cause.