Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

The call of the road : factors predicting students' car travelling intentions and behaviour

The most common daily trip for employed persons and students is the commute to and from work and/or place of study. Though there are clear environmental, health and safety benefits from using public transport instead of private vehicles for these trips, a high proportion of commuters still choose private vehicles to get to work or study. This study reports an investigation of psychological factors influencing students’ travel choices from the perspective of the Theory of Planned Behaviour (TPB). Students from 3 different university campuses (n= 186) completed a cross-sectional survey on their car commuting behaviour. Particular focus was given to whether car commuting habits could add to understanding of commuting behaviour over and above behavioural intentions. Results indicated that, as expected, behavioural intention to travel by car was the strongest TPB predictor of car commuting behaviour. Further, general car commuting habits explained additional variance over and above TPB constructs, though the contribution was modest. No relationship between habit and intentions was found. Overall results suggest that, although student car commuting behaviour is habitual in nature, it is predominantly guided by reasoned action. Implications of these findings are that in order to alter the use of private vehicles, the factors influencing commuters’ intentions to travel by car must be addressed. Specifically, interventions should target the perceived high levels of both the acceptability of commuting by car and the perceived control over the choice to commute by car.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

goDesign travelling design workshop program for regional secondary students

goDesign Travelling Workshop Program for Regional Secondary Students was an initiative of Queensland University of Technology (QUT) and the Design Institute of Australia (DIA) Queensland Branch, which aligned with the DIA unleashed: Queensland design on tour 2010 Exhibition. It was designed be delivered by university design academics in state secondary schools in Chinchilla, Mt Isa, Quilpie, Emerald, Gladstone and Bundaberg between February and September 2010, to approximately 95 secondary students and 24 teachers from the subject areas of visual art, graphics and industrial technology and design. A talk by a visiting design practitioner whose work was displayed in the exhibition, also features in the final day of the program in each town, and student work from the workshop was displayed in the exhibition alongside the professional design work. The three-day workshop is a design immersion program for regional Queensland Secondary Schools, which responds to specific actions outlined in the Queensland Government Design Strategy 2020 to ‘Build Design Knowledge and Learning’ and ‘Foster a Design Culture’. Underpinned by a place-based approach and the integration of Dr Charles Burnette’s IDESIGN teaching model, the program gives students and teachers the opportunity to explore, analyse and reimagine their local town through a series of scaffolded problem solving activities around the theme of ‘place’. The program allows students to gain hands-on experience designing graphics, products, interior spaces and architecture to assist their local community, with the support of design professionals. Students work individually and in groups on real design problems learning sketching, making, communication, presentation and collaboration skills to improve their design process, while considering social, cultural and environmental opportunities. The program was designed to facilitate an understanding of the value of design thinking and its importance to regional communities, to give students more information about various design disciplines as career options, and provide a professional development opportunity for teachers. Advisory assistance for the program was gained through Kelvin Grove State College, Queensland Studies Authority and QMI/Manufacturing Skills Queensland Manager, Manufacturing & Engineering Gateway Schools Project.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Trees along our travelling tracks

This creative non-fiction piece of writing speaks to the ‘tree’ themed edition of the About Place Journal. It begins with…“This tree stands steadfast along my inland travelling track, near the town of Mundubbera on the land of the Wakka Wakka people. It is in the region called North Burnett. When we travel, we follow the river systems and look out for distinct markers in the landscape. We acknowledge the lands of others as we move down to Booburrgan Ngmmunge (the language term used by many Aboriginal people to describe the Bunya Mountains) and beyond”. The piece includes photograph images also taken by the author.

The development of shared understandings of assessment policy : travelling between global and local contexts

In this paper, teachers’ enactment of assessment policy within demands for accountability and consistency of teacher judgements is considered. Evidence is drawn from a qualitative study involving 50 middle school teachers from Queensland, Australia, who participated in online social moderation meetings with teachers located in dispersed areas around the state. The study presents how travelling policy is embedded in local histories and cultures, in particular within systems of accountability; and the different layers of what may be considered ‘local’. The paper examines the intersections of travelling and embedded policy, and global and local contexts as these are enacted through online moderation meetings.

Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A geometric construction of travelling wave solutions to the Keller–Segel model

We study a version of the Keller–Segel model for bacterial chemotaxis, for which exact travelling wave solutions are explicitly known in the zero attractant diffusion limit. Using geometric singular perturbation theory, we construct travelling wave solutions in the small diffusion case that converge to these exact solutions in the singular limit.

Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller–Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥sqrt(2δ) in the F-KPP equation.

Travelling bones: The repatriation of Indigenous ancestral remains

In the album Journey, Archie Roach -- the Australian Indigenous singer-songwriter hailing from Mooroopna in Victoria - has a melancholy song called ‘Travell’n Bones.' It is about the repatriation of Indigenous ancestral remains to their rightful home. This Chapter considers the legal, ethical, and cultural conflicts over Australian indigenous remains being held in museums, in Australia, the United Kingdom, the European Union, and the United States. James Nason comments: ‘The explosion of legal and extra legal attention on issues of cultural property and heritage was born of the frustration and anger of indigenous peoples whose rights and perspectives about cultural property and heritage issues had been largely absent and essentially unwanted by the museum of community.' Part I focuses upon disputes in Australia involving the repatriation of Indigenous Australian remains. In Bropho v HREOC, there was controversy over a cartoon, mocking the repatriation of the remains of Yagan, an Indigenous warrior, to Western Australia. There was a discussion about the operation of the Racial Discrimination Act 1975 (Cth), and the exemptions available from the operation of the regime. Part II considers the efforts by The Te Papa Tongarewa - the Museum of New Zealand - to repatriate Maori and Moriori ancestral remains to New Zealand, and to iwi communities of origin. The conclusion considers the relevance of the United Nations Declaration on the Rights of Indigenous Persons 2007, and issues raised by ventures such as the Genographic Project.