Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Bending and blurring blended learning boundaries [Extended Abstract]

This presentation presents a blended learning model that provides greater opportunity for learning to be self-managed and personalized.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Comparing measures of fat-free mass in overweight older adults using three different bioelectrical impedance devices and three prediction equations

Objectives: To compare measures of fat-free mass (FFM) by three different bioelectrical impedance analysis (BIA) devices and to assess the agreement between three different equations validated in older adult and/or overweight populations. Design: Cross-sectional study. Setting: Orthopaedics ward of Brisbane public hospital, Australia. Participants: Twenty-two overweight, older Australians (72 yr ± 6.4, BMI 34 kg/m2 ± 5.5) with knee osteoarthritis. Measurements: Body composition was measured using three BIA devices: Tanita 300-GS (foot-to-foot), Impedimed DF50 (hand-to-foot) and Impedimed SFB7 (bioelectrical impedance spectroscopy (BIS)). Three equations for predicting FFM were selected based on their ability to be applied to an older adult and/ or overweight population. Impedance values were extracted from the hand-to-foot BIA device and included in the equations to estimate FFM. Results: The mean FFM measured by BIS (57.6 kg ± 9.1) differed significantly from those measured by foot-to-foot (54.6 kg ± 8.7) and hand-to-foot BIA (53.2 kg ± 10.5) (P < 0.001). The mean ± SD FFM predicted by three equations using raw data from hand-to-foot BIA were 54.7 kg ± 8.9, 54.7 kg ± 7.9 and 52.9 kg ± 11.05 respectively. These results did not differ from the FFM predicted by the hand-to-foot device (F = 2.66, P = 0.118). Conclusions: Our results suggest that foot-to-foot and hand-to-foot BIA may be used interchangeably in overweight older adults at the group level but due to the large limits of agreement may lead to unacceptable error in individuals. There was no difference between the three prediction equations however these results should be confirmed within a larger sample and against a reference standard.

An extended theory of planned behavior intervention for older adults With Type 2 diabetes and cardiovascular disease

A randomized controlled trial evaluated the effectiveness of a 4-wk extended theory of planned behavior (TPB) intervention to promote regular physical activity and healthy eating among older adults diagnosed with Type 2 diabetes or cardiovascular disease (N = 183). Participants completed TPB measures of attitude, subjective norm, perceived behavioral control, and intention, as well as planning and behavior, at preintervention and 1 wk and 6 wk postintervention for each behavior. No significant time-by-condition effects emerged for healthy eating. For physical activity, significant time-by-condition effects were found for behavior, intention, planning, perceived behavioral control, and subjective norm. In particular, compared with control participants, the intervention group showed short-term improvements in physical activity and planning, with further analyses indicating that the effect of the intervention on behavior was mediated by planning. The results indicate that TPB-based interventions including planning strategies may encourage physical activity among older people with diabetes and cardiovascular disease.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

The role of mindfulness in an extended TPB framework to understand drivers’ speeding intentions in school zones.

Many researchers have demonstrated the applicability of the Theory of Planned Behaviour (TPB) in predicting both intention to speed and actual speeding behaviour. However, there remain shortcomings in the explanatory power of the TPB, with research suggesting that even when drivers had reported an intention to not speed approximately 25% of drivers report behaviour that does not align with their intentions (i.e., they engaged in speeding, Elliott & Armitage, 2006). This research explores the role of a novel and promising construct, mindfulness, in enhancing the explanatory utility of the TPB for the understanding of drivers’ speeding behaviour in school zones. Mindfulness is a concept which has been widely used in studies of consciousness, but has recently been applied to the understanding of behaviour in other areas, including clinical psychology, physical activity, education and business. It has been suggested that mindfulness can also be applied to road safety, though its application within this context currently remains limited. This study was based on an e-survey of the general driving public (N=240). Overall, the results identified mindfulness as a construct which may aid understanding of the relationship between drivers’ intentions and behaviour. Theoretically, the findings may have implications in terms of identifying mindfulness as an additional explanatory construct within a TPB framework. In road safety practice, the findings suggest that efficacious countermeasures around school zones may be those that function to heighten drivers’ mindfulness, such as flashing lights and physical speed reduction measures.

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.

How to design extended finite state machine test models in Java

This chapter is a tutorial that teaches you how to design extended finite state machine (EFSM) test models for a system that you want to test. EFSM models are more powerful and expressive than simple finite state machine (FSM) models, and are one of the most commonly used styles of models for model-based testing, especially for embedded systems. There are many languages and notations in use for writing EFSM models, but in this tutorial we write our EFSM models in the familiar Java programming language. To generate tests from these EFSM models we use ModelJUnit, which is an open-source tool that supports several stochastic test generation algorithms, and we also show how to write your own model-based testing tool. We show how EFSM models can be used for unit testing and system testing of embedded systems, and for offline testing as well as online testing.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.