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.

Physical activity in three regional communities in Queensland

Objective. To describe physical activity participation in three Queensland regional communities. Design. Cross-sectional mail survey of randomly selected residents, stratified by age and sex. Setting. Esk, Mareeba and Mount Isa. Participants. 1219 (58% female) adults, with a mean age 46.7 (SD 14.7) years. Main outcome measures. Proportion of people inactive, meeting Australian activity guidelines (a minimum of 150 minutes/week and 5 sessions/week), and walking a dog daily; time spent walking and cycling for transport; location and type of recreational physical activities. Results. Overall, 18% of respondents were inactive, with the highest proportions among women (22.3%) and older adults in Mount Isa (24.3%). The proportion meeting activity guidelines was 47% with the lowest proportions among women in Mount Isa (40.4%). Although 63% reported owning a dog, only 22% reported walking a dog daily. Few people reported walking or cycling for transport. The most common types of activities were walking, home-based exercise, running/jogging, and swimming, and the most common location was at or near home. Conclusions. Physical activity levels were lower in these regional communities than the state average. The findings indicate a need for physical activity policy and intervention strategies targeting regional and rural areas. This could focus on women and older adults, dog walking, and physical activity opportunities in or near the home.

Near-Wall Turbulent Pressure Diffusion Modeling and Influence in Three-Dimensional Secondary Flows

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.

Oblique-Shock-Wave/Boundary-Layer Interaction Using Near-Wall Reynolds-Stress Models

A synthesis is presented of the predictive capability of a family of near-wall wall-normal free Reynolds stress models (which are completely independent of wall topology, i.e., of the distance fromthe wall and the normal-to-thewall orientation) for oblique-shock-wave/turbulent-boundary-layer interactions. For the purpose of comparison, results are also presented using a standard low turbulence Reynolds number k–ε closure and a Reynolds stress model that uses geometric wall normals and wall distances. Studied shock-wave Mach numbers are in the range MSW = 2.85–2.9 and incoming boundary-layer-thickness Reynolds numbers are in the range Reδ0 = 1–2×106. Computations were carefully checked for grid convergence. Comparison with measurements shows satisfactory agreement, improving on results obtained using a k–ε model, and highlights the relative importance of redistribution and diffusion closures, indicating directions for future modeling work.

Influence of inflow turbulence in shock-wave/turbulent-boundary-layer interaction computations

The influence of inflow turbulence on the results of Favre–Reynolds-averaged Navier–Stokes computations of supersonic oblique-shock-wave/turbulent-boundary-layer interactions (shock-wave Mach-number MSW ∼2.9), using seven-equation Reynolds-stress model turbulence closures, is studied. The generation of inflow conditions (and the initialization of the flowfield) for mean flow, Reynolds stresses, and turbulence length scale, based on semi-analytic grid-independent boundary-layer profiles, is described in detail. Particular emphasis is given to freestream turbulence intensity and length scale. The influence of external-flow turbulence intensity is studied in detail both for flat-plate boundary-layer flow and for a compression-ramp interaction with large separation. It is concluded that the Reynolds-stress model correctly reproduces the effects of external flow turbulence.

Integrating ICT into the planning process : impacts, opportunities and challenges

Mobile telecommunications have become a key lifestyle and technological trend of the twenty first century. In the context of increased urbanism and pressure on cites for citizen engagement for the purpose of creating good public places the potential of these technologies raises critical questions for planning professionals. Even though technology has become integral to all functions within our urban environment, little is known about perceptions and relationship between urban planners and the ubiquitous, ever-present digital layer of urban data and information. This paper explores this issue, via three focus groups and an additional follow-up interview with planners from local and state government, education and private sector. This paper explores the issues of integrating information and communication technologies into planning practice and the affordances that these technologies offer for community consultation and placemaking.

Intraurban rail access : Policy implications of five revealed perspectives from a Q-sorting exercise in three Australian cities

This project advances current understanding of intra-urban rail passengers and their travel experiences in order to help rail industry leaders tailor policy approaches to fit specific, relevant segments of their target population. Using a Q sorting technique and cluster analysis, our preliminary research identified five perspectives occurring in a small sample of rail passengers, who varied in their frequency and location of rail travel as well as certain socio-demographic characteristics. Revealed perspectives (named to capture the gist of their content) included: ‘Rail Travel is About the Destination, Not the Journey’; ‘Despite Challenges, Public Transport is Still the Best Option’; ‘Rail Travel is Fine’; ‘Rail Travel? So Far, So Good’; and ‘Bad Taste for Rail Travel’. This paper discusses each of the perspectives in detail, and considers them in terms of tailored policy implications. An overarching finding from this study is that improving railway travel ‘access’ requires attention to physical, psychological, financial, and social facets of accessibility. For example, designing waiting areas to be more socially functional and comfortable has the potential to increase ridership by addressing social forms of access, decreasing perceived wait times, and making time at the station feel like time well spent. Even at this preliminary stage, the Q sorting technique promises to provide a valuable, holistic albeit fine-grained analysis of passenger attitudes and experiences that will assist industry efforts to increase ridership.

Linking three-dimensional geological modelling and multivariate statistical analysis to define groundwater chemistry baseline and identify inter-aquifer connectivity within the Clarence-Moreton Basin, Southeast Queensland, Australia

The Clarence-Moreton Basin (CMB) covers approximately 26000 km2 and is the only sub-basin of the Great Artesian Basin (GAB) in which there is flow to both the south-west and the east, although flow to the south-west is predominant. In many parts of the basin, including catchments of the Bremer, Logan and upper Condamine Rivers in southeast Queensland, the Walloon Coal Measures are under exploration for Coal Seam Gas (CSG). In order to assess spatial variations in groundwater flow and hydrochemistry at a basin-wide scale, a 3D hydrogeological model of the Queensland section of the CMB has been developed using GoCAD modelling software. Prior to any large-scale CSG extraction, it is essential to understand the existing hydrochemical character of the different aquifers and to establish any potential linkage. To effectively use the large amount of water chemistry data existing for assessment of hydrochemical evolution within the different lithostratigraphic units, multivariate statistical techniques were employed.

Analysis of heat transfer and fluid flow in a triangular enclosure in presence of an adiabatic fin

Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.

An evolutionary computation approach to three-dimensional path planning for unmanned aerial vehicles with tactical and kinematic constraints

This paper presents a novel evolutionary computation approach to three-dimensional path planning for unmanned aerial vehicles (UAVs) with tactical and kinematic constraints. A genetic algorithm (GA) is modified and extended for path planning. Two GAs are seeded at the initial and final positions with a common objective to minimise their distance apart under given UAV constraints. This is accomplished by the synchronous optimisation of subsequent control vectors. The proposed evolutionary computation approach is called synchronous genetic algorithm (SGA). The sequence of control vectors generated by the SGA constitutes to a near-optimal path plan. The resulting path plan exhibits no discontinuity when transitioning from curve to straight trajectories. Experiments and results show that the paths generated by the SGA are within 2% of the optimal solution. Such a path planner when implemented on a hardware accelerator, such as field programmable gate array chips, can be used in the UAV as on-board replanner, as well as in ground station systems for assisting in high precision planning and modelling of mission scenarios.

Integrated TEM, XRD and electron-microprobe investigation of mixed-layer chlorite smectite from the Point-Sal ophiolite, California

Five basalt samples from the Point Sal ophiolite, California, were examined using HRTEM and AEM in order to compare observations with interpretations of XRD patterns and microprobe analyses. XRD data from ethylene-glycol-saturated samples indicate the following percentages of chlorite in mixed-layer chlorite-smectite identified for each specimen: (i) L2036 almost-equal-to 50%, (ii) L2035 almost-equal-to 70 and 20%, (iii) 1A-13 almost-equal-to 70%, (iv) 1B-42 almost-equal-to 70%, and (v) 1B-55 = 100%. Detailed electron microprobe analyses show that 'chlorite' analyses with high Si, K, Na and Ca contents are the result of interlayering with smectite-like layers. The Fe/(Fe + Mg) ratios of mixed-layer phyllosilicates from Point Sal samples are influenced by the bulk rock composition, not by the percentage of chlorite nor the structure of the phyllosilicate. Measurements of lattice-fringe images indicate that both smectite and chlorite layers are present in the Point Sal samples in abundances similar to those predicted with XRD techniques and that regular alternation of chlorite and smectite occurs at the unit-cell scale. Both 10- and 14-angstrom layers were recorded with HRTEM and interpreted to be smectite and chlorite, respectively. Regular alternation of chlorite and smectite (24-angstrom periodicity) occurs in upper lava samples L2036 and 1A-13, and lower lava sample 1B-42 for as many as seven alternations per crystallite with local layer mistakes. Sample L2035 shows disordered alternation of chlorite and smectite, with juxtaposition of smectite-like layers, suggesting that randomly interlayered chlorite (< 0.5)-smectite exists. Images of lower lava sample 1B-55 show predominantly 14-angstrom layers. Units of 24 angstrom tend to cluster in what may otherwise appear to be disordered mixtures, suggesting the existence of a corrensite end-member having thermodynamic significance.