Velocity jump processes with proliferation

Cell invasion involves a population of cells that migrate along a substrate and proliferate to a carrying capacity density. These two processes, combined, lead to invasion fronts that move into unoccupied tissues. Traditional modelling approaches based on reaction–diffusion equations cannot incorporate individual–level observations of cell velocity, as information propagates with infinite velocity according to these parabolic models. In contrast, velocity jump processes allow us to explicitly incorporate individual–level observations of cell velocity, thus providing an alternative framework for modelling cell invasion. Here, we introduce proliferation into a standard velocity–jump process and show that the standard model does not support invasion fronts. Instead, we find that crowding effects must be explicitly incorporated into a proliferative velocity–jump process before invasion fronts can be observed. Our observations are supported by numerical and analytical solutions of a novel coupled system of partial differential equations, including travelling wave solutions, and associated random walk simulations.

Modeling heat and mass transfer process during convection drying of fruit

Fruit drying is a process of removing moisture to preserve fruits by preventing microbial spoilage. It increases shelf life, reduce weight and volume thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. But, it is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the material. In this background, the aim of this paper to develop a mathematical model to simulate coupled heat and mass transfer during convective drying of fruit. This model can be used predict the temperature and moisture distribution inside the fruits during drying. Two models were developed considering shrinkage dependent and temperature dependent moisture diffusivity and the results were compared. The governing equations of heat and mass transfer are solved and a parametric study has been done with Comsol Multiphysics 4.3. The predicted results were validated with experimental data.

An ingenuous Decision Support System (iDSS) approach for remote area pregnant women

This paper addresses development of an ingenious decision support system (iDSS) based on the methodology of survey instruments and identification of significant variables to be used in iDSS using statistical analysis. A survey was undertaken with pregnant women and factorial experimental design was chosen to acquire sample size. Variables with good reliability in any one of the statistical techniques such as Chi-square, Cronbach’s α and Classification Tree were incorporated in the iDSS. The ingenious decision support system was implemented with Visual Basic as front end and Microsoft SQL server management as backend. Outcome of the ingenious decision support system include advice on Symptoms, Diet and Exercise to pregnant women.

Multiphysics modelling of convective drying of food materials

Currently, 1.3 billion tonnes of food is lost annually due to lack of proper processing and preservation method. Drying is one of the easiest and oldest methods of food processing which can contribute to reduce that huge losses, combat hunger and promote food security. Drying increase shelf life, reduce weight and volume of food thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. However, drying is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the food material. Modelling of this process is essential to optimize the drying kinetics and improve energy efficiency of the process. Since material properties varies with moisture content, the models should not consider constant materials properties, constant diffusion .The objective of this paper is to develop a multiphysics based mathematical model to simulate coupled heat and mass transfer during convective drying of fruit considering variable material properties. This model can be used predict the temperature and moisture distribution inside the food during drying. Effect of different drying air temperature and drying air velocity on drying kinetics has been demonstrated. The governing equations of heat and mass transfer were solved with Comsol Multiphysics 4.3.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Emotional arousal of beginning physics teachers during extended experimental investigations

Teachers often have difficulty implementing inquiry-based activities, leading to the arousal of negative emotions. In this multicase study of beginning physics teachers in Australia, we were interested in the extent to which their expectations were realized and how their classroom experiences while implementing extended experimental investigations (EEIs) produced emotional states that mediated their teaching practices. Against rhetoric of fear expressed by their senior colleagues, three of the four teachers were surprised by the positive outcomes from their supervision of EEIs for the first time. Two of these teachers experienced high intensity positive emotions in response to their students’ success. When student actions / outcomes did not meet their teachers’ expectations, frustration, anger, and disappointment were experienced by the teachers, as predicted by a sociological theory of human emotions (Turner, 2007). Over the course of the EEI projects, the teachers’ practices changed along with their emotional states and their students’ achievements. We account for similarities and differences in the teachers’ emotional experiences in terms of context, prior experience, and expectations. The findings from this study provide insights into effective supervision practices that can be used to inform new and experienced teachers alike.

Numerical simulation of red blood cells’ motion : a review

The micro-circulation of blood plays an important role in human body by providing oxygen and nutrients to the cells and removing carbon dioxide and wastes from the cells. This process is greatly affected by the rheological properties of the Red Blood Cells (RBCs). Changes in the rheological properties of the RBCs are caused by certain human diseases such as malaria and sickle cell diseases. Therefore it is important to understand the motion and deformation mechanism of RBCs in order to diagnose and treat this kind of diseases. Although, many methods have been developed to explore the behavior of the RBCs in micro-channels, they could not explain the deformation mechanism of the RBCs properly. Recently developed Particle Methods are employed to explain the RBCs’ behavior in micro-channels more comprehensively. The main objective of this study is to critically analyze the present methods, used to model the RBC behavior in micro-channels, in order to develop a computationally efficient particle based model to describe the complete behavior of the RBCs in micro-channels accurately and comprehensively

Orthopaedics and Trauma Queensland Annual Report 2011

Orthopaedics and Trauma Queensland, a Centre for Research and Education in Musculoskeletal Disorders, is an internationally recognised research group that is developing into an international leader in research and education. It provides a stimulus for research, education and clinical application within the international orthopaedic and trauma communities. Orthopaedics and Trauma Queensland develops and promotes the innovative use of engineering and technology, in collaboration with surgeons, to provide new techniques, materials, procedures and medical devices. Its integration with clinical practice and strong links with hospitals ensure that the research will be translated into practical outcomes for patients. The group undertakes clinical practice in orthopaedics and trauma and applies core engineering skills to challenges in medicine. The research is built on a strong foundation of knowledge in biomedical engineering, and incorporates expertise in cell biology, mathematical modelling, human anatomy and physiology and clinical medicine in orthopaedics and trauma. New knowledge is being developed and applied to the full range of orthopaedic diseases and injuries, such as knee and hip replacements, fractures and spinal deformities.

Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Patient-specific simulations of spinal deformity surgery

Adolescent idiopathic scoliosis (AIS) is a three-dimensional spinal deformity involving the side-to-side curvature of the spine in the coronal plane and axial rotation of the vertebrae in the transverse plane. For patients with a severe or rapidly progressing deformity, corrective instrumented fusion surgery is performed. The wide choice of implants and large variability between patients make it difficult for surgeons to choose optimal treatment strategies. This paper describes the patient specific finite element modelling techniques employed and the results of preliminary analyses predicting the surgical outcomes for a series of AIS patients. This report highlights the importance of not only patient-specific anatomy and material parameters, but also patient-specific data for the clinical and physiological loading conditions experienced by the patient who has corrective scoliosis surgery.

Morphology-based model for predicting osteocyte-like cell line (MLO-Y4) growth process

This work has led to the development of empirical mathematical models to quantitatively predicate the changes of morphology in osteocyte-like cell lines (MLO-Y4) in culture. MLO-Y4 cells were cultured at low density and the changes in morphology recorded over 11 hours. Cell area and three dimensional shape features including aspect ratio, circularity and solidity were then determined using widely accepted image analysis software (ImageJTM). Based on the data obtained from the imaging analysis, mathematical models were developed using the non-linear regression method. The developed mathematical models accurately predict the morphology of MLO-Y4 cells for different culture times and can, therefore, be used as a reference model for analyzing MLO-Y4 cell morphology changes within various biological/mechanical studies, as necessary.

A novel testing system for a Cycloidal drive

At present, for mechanical power transmission, Cycloidal drives are most preferred - for compact, high transmission ratio speed reduction, especially for robot joints and manipulator applications. Research on drive-train dynamics of Cycloidal drives is not well-established. This paper presents a testing rig for Cycloidal drives, which would produce data for development of mathematical models and investigation of drive-train dynamics, further aiding in optimising its design

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

"You help me improve my English, I'll teach you Physics!" Cuban teachers overseas

Lending teachers for two-year periods is one of the ways in which Cuba has been able to collaborate with other countries in their efforts to improve educational planning and practice. My field research in 2001 in Jamaica (March and November) and in Namibia (December) enabled me to obtain information about how Cuban teachers are being utilized, and about the educational implications of this project. In Jamaica, I interviewed 15 Cuban teachers in several schools and one in the vocational institute, as well as the Cuban project supervisor in charge of the 51 Cuban teachers. I also talked with officials at the Jamaican Ministry of Education to obtain an idea of the developmental needs in the various subjects that the Cubans had been asked to teach. In Namibia I interviewed personnel in the National Sports Directorate and the Cuban manager in charge of the sports education project. The chapter draws on these interviews to build a picture of how the program of collaboration is organized, and considers its postcolonial significance, in theory and in practice, as an example of South-South collaboration. The chapter contributes to a multilevel style of comparative education analysis based on microlevel qualitative fieldwork within a framework that compares cross-cultural issues and national policies. The discussion of the educational situation of the host countries suggests why Cuban teachers can contribute to meeting curricular needs, particularly in the areas of the sciences, mathematics, Spanish, and sports. The friendly and joking remark of one of the Cuban teachers to school students in Jamaica: “You help me improve my English, I’ll teach you Physics!” highlights the reciprocal potential of these cooperation projects, discussed in several chapters of this book.