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.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

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.

Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system

We investigate regions of bistability between different travelling and stationary structures in a planar singularly-perturbed three-component reaction-diffusion system that arises in the context of gas discharge systems. In previous work, we delineated the existence and stabil-ity regions of stationary localized spots in this system. Here, we complement this analysis by establishing the stability regions of planar travelling fronts and stationary stripes. Taken together, these results imply that stable fronts and spots can coexist in three-component systems. Numerical simulations indicate that the stable fronts never move towards stable spots but instead move away from them.

Reasoning about component similarity in building product models from the construction perspective

Identifying the design features that impact construction is essential to developing cost effective and constructible designs. The similarity of building components is a critical design feature that affects method selection, productivity, and ultimately construction cost and schedule performance. However, there is limited understanding of what constitutes similarity in the design of building components and limited computer-based support to identify this feature in a building product model. This paper contributes a feature-based framework for representing and reasoning about component similarity that builds on ontological modelling, model-based reasoning and cluster analysis techniques. It describes the ontology we developed to characterize component similarity in terms of the component attributes, the direction, and the degree of variation. It also describes the generic reasoning process we formalized to identify component similarity in a standard product model based on practitioners' varied preferences. The generic reasoning process evaluates the geometric, topological, and symbolic similarities between components, creates groupings of similar components, and quantifies the degree of similarity. We implemented this reasoning process in a prototype cost estimating application, which creates and maintains cost estimates based on a building product model. Validation studies of the prototype system provide evidence that the framework is general and enables a more accurate and efficient cost estimating process.

Work-integrated learning courses : an essential component for preparing students to work in statutory child protection?

Undergraduate programs can play an important role in the development of individuals wanting professional employment within statutory child protection agencies: both the coursework and the work-integrated learning (WIL) components of degrees have a role in this process. This paper uses a collective case study methodology to examine the perceptions and experiences of first year practitioners within a specific statutory child protection agency in order to identify if they felt prepared for their current role. The sample of 20 participants came from a range of discipline backgrounds with just over half of the sample (55 per cent) completing a WIL placement as part of their undergraduate studies. The results indicate that while some participants were able to identify and articulate specific benefits from their undergraduate coursework studies all participants who had undertaken a WIL placement as part of their degree believed the WIL placement was beneficial for their current work.

Condition-based maintenance optimisation without a predetermined strategy structure for a two-component series system

Most existing research on maintenance optimisation for multi-component systems only considers the lifetime distribution of the components. When the condition-based maintenance (CBM) strategy is adopted for multi-component systems, the strategy structure becomes complex due to the large number of component states and their combinations. Consequently, some predetermined maintenance strategy structures are often assumed before the maintenance optimisation of a multi-component system in a CBM context. Developing these predetermined strategy structure needs expert experience and the optimality of these strategies is often not proofed. This paper proposed a maintenance optimisation method that does not require any predetermined strategy structure for a two-component series system. The proposed method is developed based on the semi-Markov decision process (SMDP). A simulation study shows that the proposed method can identify the optimal maintenance strategy adaptively for different maintenance costs and parameters of degradation processes. The optimal maintenance strategy structure is also investigated in the simulation study, which provides reference for further research in maintenance optimisation of multi-component systems.

Quantitative and qualitative assessment of the regenerative potential of osteoblasts versus bone marrow derived mesenchymal stem cells in the reconstruction of critical sized segmental tibial bone defects in a large animal model

This thesis is about the use of different cells for bone tissue engineering. The cells were used in combination with a novel biomaterial in a large tibial bone defects in a sheep model. Furthermore this study developed a novel cell delivery procedure for bone tissue engineering. This novel procedure of cell delivery could overcome the current problems of cell-based tissue engineering and serve as a baseline for the translation of novel concepts into clinical application.

Principal component and linkage analysis of cardiovascular risk traits in the Norfolk isolate

OBJECTIVE(S): An individual's risk of developing cardiovascular disease (CVD) is influenced by genetic factors. This study focussed on mapping genetic loci for CVD-risk traits in a unique population isolate derived from Norfolk Island. METHODS: This investigation focussed on 377 individuals descended from the population founders. Principal component analysis was used to extract orthogonal components from 11 cardiovascular risk traits. Multipoint variance component methods were used to assess genome-wide linkage using SOLAR to the derived factors. A total of 285 of the 377 related individuals were informative for linkage analysis. RESULTS: A total of 4 principal components accounting for 83% of the total variance were derived. Principal component 1 was loaded with body size indicators; principal component 2 with body size, cholesterol and triglyceride levels; principal component 3 with the blood pressures; and principal component 4 with LDL-cholesterol and total cholesterol levels. Suggestive evidence of linkage for principal component 2 (h(2) = 0.35) was observed on chromosome 5q35 (LOD = 1.85; p = 0.0008). While peak regions on chromosome 10p11.2 (LOD = 1.27; p = 0.005) and 12q13 (LOD = 1.63; p = 0.003) were observed to segregate with principal components 1 (h(2) = 0.33) and 4 (h(2) = 0.42), respectively. CONCLUSION(S): This study investigated a number of CVD risk traits in a unique isolated population. Findings support the clustering of CVD risk traits and provide interesting evidence of a region on chromosome 5q35 segregating with weight, waist circumference, HDL-c and total triglyceride levels.

Evidence for an X-linked genetic component in familial typical migraine

Migraine is a common complex disorder that shows strong familial aggregation. There is a general increased prevalence of migraine in females compared with males, with recent studies indicating that migraine affects 18% of females compared with 6% of males. This preponderance of females among migraine sufferers coupled with evidence of an increased risk of migraine in first degree relatives of male probands but not in relatives of female probands suggests the possibility of an X-linked dominant gene. We report here the localization of a typical migraine susceptibility locus to the X chromosome. Of three large multigenerational migraine pedigrees two families showed significant excess allele sharing to Xq markers (P = 0.031 and P = 0.012). Overall analysis of data from all three pedigrees gave significant evidence in support of linkage and heterogeneity (HLOD = 3.1). These findings provide conclusive evidence that familial typical migraine is a heterogeneous disorder. We suggest that the localization of a migraine susceptibility locus to the X chromosome could in part explain the increased risk of migraine in relatives of male probands and may be involved in the increased female prevalence of this disorder.

Development of school connectedness as a component of an injury prevention program for early adolescents

The current program of research addresses the need for multi-level programs to target the major increase in injury rates that occurs throughout adolescence. Specifically, it involves the investigation of school connectedness as a protective factor for adolescent injury, and the development of school connectedness as a component of an injury prevention program. To date, school-based risk taking and injury prevention has frequently been limited to addressing adolescents' knowledge and attitudes to risk behaviours, and has largely overlooked the importance of the wider school social context as a protective factor in adolescent development. Additionally, school connectedness has been primarily studied in terms of its impact on student achievement, wellbeing and risk taking behaviour, and research has not yet addressed possible links with injury. Further, school connectedness intervention programs have targeted risk taking behaviours without evaluating their potential impact on injury outcomes. This is the first reported research to develop strategies to increase school connectedness as part of a school-based injury prevention program. The research program was conceptualised as three distinct stages. The development of these research stages was informed by a comprehensive review of the literature on adolescent risk taking, injury and school-based prevention, as well as on school connectedness and its importance in adolescence. A review of the school connectedness literature indicated that students' connectedness is largely influenced by relationships within the school context including with teachers and other school staff, and is therefore a potentially modifiable factor that may be targeted in school-based programs. Overall, the literature shows school connectedness to be a key protective factor in adolescent development. This review established a foundation from which the current program of research was designed. The first stage of the research involved an empirical investigation of the relationship between adolescent risk taking-related injuries and school connectedness. Stage one incorporated two studies. The first involved the development of a measure of adolescent injury, the Extended Adolescent Injury Checklist (E-AIC), for use in the current research as well as in future school-based studies and program evaluation. The results of this study also highlighted the extent of the problem of risk-related injury in adolescence. The second study in Stage one examined the relationship between students' reports of school connectedness, risk taking behaviour and risk taking-related injuries on the E-AIC. The results of this study showed significant relationships between increased school connectedness and reduced reported engagement in transport and violence risk taking, and fewer associated injuries. This study therefore suggested the potential for school-based injury prevention programs to incorporate strategies targeting increased adolescent connectedness to school. The second stage of this research involved the compilation of an evidence base to inform the design of a school connectedness intervention. Stage two also incorporated two studies. The first study in Stage two involved a systematic review of programs that have targeted school connectedness for reduced risk taking and injury. The results of this study revealed that interventions targeting school connectedness can be effective in reducing adolescent risk taking behaviour, and also provided an evidence base for the design of the current school connectedness intervention. The second study in Stage two examined teachers' understanding and perceptions of school connectedness. This qualitative study indicated that teachers consider students' connectedness to be an important factor that relates to their risk taking behaviour; and also provided directions and content for the intervention design stage. The third stage of this research built upon the findings of each of the previous studies, and involved the design, implementation and evaluation of a school connectedness intervention as a component of an adolescent injury prevention program, Skills for Preventing Injury in Youth (SPIY). This connectedness intervention was designed as a professional development workshop for teachers of 13 to 14 year old adolescents, and was developed as a complementary component to the curriculum-based SPIY program. The SPIY connectedness component was implemented and evaluated using process and six-month impact evaluation methodologies. The results of this study revealed that teachers saw value in the program and made use of the strategies presented, and that program school students' self-reported violence risk behaviour was reduced at six-month follow-up. Despite these promising findings, the results of this study did not demonstrate a significant impact of the program on change in students' connectedness to school, relative to comparison schools. The positive impact on self-reported violence risk behaviour was however replicated in additional analyses comparing students participating in the connectedness version of SPIY with students participating in an earlier curriculumonly version of the program. This finding indicated that the connectedness component has additional benefits relating to reduction in violence risks, over and above a curriculum-only version of the program. This research was the first reported to address the relationship between school connectedness and adolescent injury outcomes, and to develop school connectedness as a component of an adolescent injury prevention program. Overall, the results of this program of research have demonstrated the importance of incorporating strategies targeting the wider school social context, including school connectedness, in adolescent injury prevention programs. This research has important implications for future research and practice in adolescent injury prevention.

A new efficiency model for a regenerative dynamometer

This paper presents two efficiency models for the regenerative dynamometer to be built at the University of Queensland. The models incorporate an accurate accounting of the losses associated with the regenerative dynamometer and the battery modelling technique used. In addition to the models the cycle and instantaneous efficiencies were defined for a regenerative system that requires a desired torque output. The simulation of the models allowed the instantaneous and cycle efficiencies to be examined. The results show the intended dynamometer machine has significant efficiency draw backs but incorporating field winding control, the efficiency can be improved.

Selection of energy storage system for a regenerative dynamic dynamometer

This paper presents a design technique of a fully regenerative dynamic dynamometer. It incorporates an energy storage system to absorb the energy variation due to dynamometer transients. This allows the minimum power electronics requirement at the grid to supply the losses. The simulation results of the full system over a driving cycle show the amount of energy required to complete a driving cycle, therefore the size of the energy storage system can be determined.

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.