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.

Mathematical modeling of the cancer cell’s control circuitry : paving the way to individualized therapeutic strategies

Cancer is a disease of signal transduction in which the dysregulation of the network of intracellular and extracellular signaling cascades is sufficient to thwart the cells finely-tuned biochemical control mechanisms. A keen interest in the mathematical modeling of cell signaling networks and the regulation of signal transduction has emerged in recent years, and has produced a glimmer of insight into the sophisticated feedback control and network regulation operating within cells. In this review, we present an overview of published theoretical studies on the control aspects of signal transduction, emphasizing the role and importance of mechanisms such as ‘ultrasensitivity’ and feedback loops. We emphasize that these exquisite and often subtle control strategies represent the key to orchestrating ‘simple’ signaling behaviors within the complex intracellular network, while regulating the trade-off between sensitivity and robustness to internal and external perturbations. Through a consideration of these apparent paradoxes, we explore how the basic homeostasis of the intracellular signaling network, in the face of carcinogenesis, can lead to neoplastic progression rather than cell death. A simple mathematical model is presented, furnishing a vivid illustration of how ‘control-oriented’ models of the deranged signaling networks in cancer cells may enucleate improved treatment strategies, including patient-tailored combination therapies, with the potential for reduced toxicity and more robust and potent antitumor activity.

Using mathematical modelling to evaluate drivers and predict trajectories of HIV and STI epidemics in South East Asian and Australian populations

Objective To evaluate the potential impact of the current global economic crisis (GEC) on the spread of HIV. Design To evaluate the impact of the economic downturn we studied two distinct HIV epidemics in Southeast Asia: the generalized epidemic in Cambodia where incidence is declining and the epidemic in Papua New Guinea (PNG) which is in an expansion phase. Methods Major HIV-related risk factors that may change due to the GEC were identified and a dynamic mathematical transmission model was developed and used to forecast HIV prevalence, diagnoses, and incidence in Cambodia and PNG over the next 3 years. Results In Cambodia, the total numbers of HIV diagnoses are not expected to be largely affected. However, an estimated increase of up to 10% in incident cases of HIV, due to potential changes in behavior, may not be observed by the surveillance system. In PNG, HIV incidence and diagnoses could be more affected by the GEC, resulting in respective increases of up to 17% and 11% over the next 3 years. Decreases in VCT and education programs are the factors that may be of greatest concern in both settings. A reduction in the rollout of antiretroviral therapy could increase the number of AIDS-related deaths (by up to 7.5% after 3 years). Conclusions The GEC is likely to have a modest impact on HIV epidemics. However, there are plausible conditions under which the economic downturns can noticeably influence epidemic trends. This study highlights the high importance of maintaining funding for HIV programs.

Mathematical modelling and experimental validation of solar assisted heat pump system

Singapore is located at the equator, with abundant supply of solar radiation, relatively high ambient temperature and relative humidity throughout the year. The meteorological conditions of Singapore are favourable for efficient operation of solar energy based systems. Solar assisted heat pump systems are built on the roof-top of National University of Singapore’s Faculty of Engineering. The objectives of this study include the design and performance evaluation of a solar assisted heat-pump system for water desalination, water heating and drying of clothes. Using MATLAB programming language, a 2-dimensional simulation model has been developed to conduct parametric studies on the system. The system shows good prospect to be implemented in both industrial and residential applications and would give new opportunities in replacing conventional energy sources with green renewable energy.

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

Mathematical modelling of fumigant transport in stored grain

Computational fluid dynamics, analytical solutions, and mathematical modelling approaches are used to gain insights into the distribution of fumigant gas within farm-scale, grain storage silos. Both fan-forced and tablet fumigation are considered in this work, which develops new models for use by researchers, primary producers and silo manufacturers to assist in the eradication grain storage pests.

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

A framework for model integration and holistic modelling of socio-technical systems

This paper presents a layered framework for the purposes of integrating different Socio-Technical Systems (STS) models and perspectives into a whole-of-systems model. Holistic modelling plays a critical role in the engineering of STS due to the interplay between social and technical elements within these systems and resulting emergent behaviour. The framework decomposes STS models into components, where each component is either a static object, dynamic object or behavioural object. Based on existing literature, a classification of the different elements that make up STS, whether it be a social, technical or a natural environment element, is developed; each object can in turn be classified according to the STS elements it represents. Using the proposed framework, it is possible to systematically decompose models to an extent such that points of interface can be identified and the contextual factors required in transforming the component of one model to interface into another is obtained. Using an airport inbound passenger facilitation process as a case study socio-technical system, three different models are analysed: a Business Process Modelling Notation (BPMN) model, Hybrid Queue-based Bayesian Network (HQBN) model and an Agent Based Model (ABM). It is found that the framework enables the modeller to identify non-trivial interface points such as between the spatial interactions of an ABM and the causal reasoning of a HQBN, and between the process activity representation of a BPMN and simulated behavioural performance in a HQBN. Such a framework is a necessary enabler in order to integrate different modelling approaches in understanding and managing STS.

Mathematical models of calcium and tight junctions in normal and reconstructed epidermis

This project investigated the calcium distributions of the skin, and the growth patterns of skin substitutes grown in the laboratory, using mathematical models. The research found that the calcium distribution in the upper layer of the skin is controlled by three different mechanisms, not one as previously thought. The research also suggests that tight junctions, which are adhesions between neighbouring skin cells, cannot be solely responsible for the differences in the growth patterns of skin substitutes and normal skin.

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.