Ecological dynamics as a theoretical framework for development of sustainable behaviours towards the environment

This paper proposes how the theoretical framework of ecological dynamics can provide an influential model of the learner and the learning process to pre-empt effective behaviour changes. Here we argue that ecological dynamics supports a well established model of the learner ideally suited to the environmental education context because of its emphasis on the learner-environment relationship. The model stems from perspectives on behaviour change in ecological psychology and dynamical systems theory. The salient points of the model are highlighted for educators interested in manipulating environmental constraints in the learning process, with the aim of designing effective learning programs in environmental education. We conclude by providing generic principles of application which might define the learning process in environmental education programs.

The effect of ribbing on the energy flow between two rectangular plates coupled at right angle

This paper presents an analytical model to study the effect of stiffening ribs on vibration transmission between two rectangular plates coupled at right angle. Interesting wave attenuation patterns were observed by placing the stiffening rib either on the source or on the receiving plate. The result can be used to improve the understanding of vibration and for vibration control of more complex structures such as transformer tanks and machine covers.

Self-assembled hyperbranched polymer - gold nanoparticle hybrids : understanding the effect of polymer coverage on assembly size and SERS performance

In the past few years, remarkable progress has been made in unveiling novel and unique optical properties of strongly coupled plasmonic nanostructures. However, application of such plasmonic nanostructures in biomedicine remains challenging due to the lack of facile and robust assembly methods for producing stable nanostructures. Previous attempts to achieve plasmonic nano-assemblies using molecular ligands were limited due to the lack of flexibility that could be exercised in forming them. Here, we report the utilization of tailor-made hyperbranched polymers (HBP) as linkers to assemble gold nanoparticles (NPs) into nano-assemblies. The ease and flexibility in tuning the particle size and number of branch ends of a HBP makes it an ideal candidate as a linker, as opposed to DNA, small organic molecules and linear or dendrimeric polymers. We report a strong correlation of polymer (HBP) concentration with the size of the hybrid nano-assemblies and “hot-spot” density. We have shown that such solutions of stable HBP-gold nano-assemblies can be barcoded with various Raman tags to provide improved surface-enhanced Raman scattering (SERS) compared with non-aggregated NP systems. These Raman barcoded hybrid nano-assemblies, with further optimization of NP shape, size and “hot-spot” density, may find application as diagnostic tools in nanomedicine.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.

Interacting constraints shape emergent decision-making of referees

How and why football referees made decisions was investigated. A constructivist grounded theory methodology was undertaken to tap into the experiential knowledge of referees. The participant cohort comprised 7 A-League referees (aged 23 to 35) and 8 local Brisbane league referees (aged 20 to 50), spanning the lowest to highest levels of competition in men’s football in Australia. Results found that referees used ‘four pillars’ to underpin their judgments, these were conceptual notions of: safety, fairness, accuracy and entertainment. A fifth pillar ‘consistency’ referred to the referee’s ‘contextual sensitivity’. Results were explained using an ecological dynamics framework that emphasises the individual-environment scale of analysis. It was concluded that interacting constraints shape emergent decision-making in referees which are nested in task goals.

Acquisition of expertise in cricket fast bowling : perceptions of expert players and coaches

Objectives: Experiential knowledge of elite athletes and coaches was investigated to reveal insights on expertise acquisition in cricket fast bowling. Design: Twenty-one past or present elite cricket fast bowlers and coaches of national or international level were interviewed using an in-depth, open-ended, semi-structured approach. Methods: Participants were asked about specific factors which they believed were markers of fast bowling expertise potential. Of specific interest was the relative importance of each potential component of fast bowling expertise and how components interacted or developed over time. Results: The importance of intrinsic motivation early in development was highlighted, along with physical, psychological and technical attributes. Results supported a multiplicative and interactive complex systems model of talent development in fast bowling, in which component weightings were varied due to individual differences in potential experts. Dropout rates in potential experts were attributed to misconceived current talent identification programmes and coaching practices, early maturation and physical attributes, injuries and lack of key psychological attributes and skills. Conclusions: Data are consistent with a dynamical systems model of expertise acquisition in fast bowling, with numerous trajectories available for talent development. Further work is needed to relate experiential and theoretical knowledge on expertise in other sports.

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.

A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab.

Biogas in Bangladesh : challenges and strategies

The people of Bangladesh are underprivileged from continuous grid electricity. Despite the plentiful supply of renewable sources of energy in Bangladesh, currently their contribution to the electricity supply remains inconsequential. Use of renewable energy is considered an indispensable component of sustainable energy systems, as renewable energy resources emit less greenhouse gas emissions compared to other non-renewable energy systems. Out of the various renewable sources, solar and biogas and to a limited extend, wind and hydro-power are effectively used. Though the biogas production was the leading and most appropriate renewable energy resource in our country, it has become notably insignificant due to the lack of appropriate strategies and institutional settings. To address this, this article examines Bangladesh's current energy strategies and institutional settings and investigates future strategies for the advancement of biogas production. This article argues that further significant efforts could be made toward energy sustainability in Bangladesh and the development for a national sustainable energy policy.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Injection velocity control of thermoplastic injection molding via a double controller scheme

Injection velocity has been recognized as a key variable in thermoplastic injection molding. Its closed-loop control is, however, difficult due to the complexity of the process dynamic characteristics. The basic requirements of the control system include tracking of a pre-determined injection velocity curve defined in a profile, load rejection and robustness. It is difficult for a conventional control scheme to meet all these requirements. Injection velocity dynamics are first analyzed in this paper. Then a novel double-controller scheme is adopted for the injection velocity control. This scheme allows an independent design of set-point tracking and load rejection and has good system robustness. The implementation of the double-controller scheme for injection velocity control is discussed. Special techniques such as profile transformation and shifting are also introduced to improve the velocity responses. The proposed velocity control has been experimentally demonstrated to be effective for a wide range of processing conditions.

Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.