Planar radial spots in a three-component FitzHugh-Nagumo system

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

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.

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.

Design and modification of three-component randomly incorporated copolymers for high performance organic photovoltaic applications

In this study we report the molecular design, synthesis, characterization, and photovoltaic properties of a series of diketopyrrolopyrrole (DPP) and dithienothiophene (DTT) based donor-acceptor random copolymers. The six random copolymers are obtained via Stille coupling polymerization using various concentration ratios of donor to acceptor in the conjugated backbone. Bis(trimethylstannyl)thiophene was used as the bridge block to link randomly with the two comonomers 5-(bromothien-2-yl)-2,5-dialkylpyrrolo[3,4-c]pyrrole-1, 4-dione and 2,6-dibromo-3,5-dipentadecyl-dithieno[3,2-b;2′,3′-d] thiophene. The optical properties of these copolymers clearly reveal a change in the absorption band through optimization of the donor-acceptor ratio in the backbone. Additionally, the solution processability of the copolymers is modified through the attachment of different bulky alkyl chains to the lactam N-atoms of the DPP moiety. Applications of the polymers as light-harvesting and electron-donating materials in solar cells, in conjunction with PCBM as acceptor, show power conversion efficiencies (PCEs) of up to 5.02%.

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.

QUT speaker identity verification system for EVALITA 2009

This document outlines the system submitted by the Speech and Audio Research Laboratory at the Queensland University of Technology (QUT) for the Speaker Identity Verication: Application task of EVALITA 2009. This submission consisted of a score-level fusion of three component systems, a joint-factor GMM system and two SVM systems using GLDS and GMM supervector kernels. Development and evaluation results are presented, demonstrating the effectiveness of this fused system approach.

Towards a new model of successful faking

Existing literature has failed to find robust relationships between individual differences and the ability to fake psychological tests, possibly due to limitations in how successful faking is operationalised. In order to fake, individuals must alter their original profile to create a particular impression. Currently, successful faking is operationalised through statistical definitions, informant ratings, known groups comparisons, the use of archival and baseline data, and breaches of validity indexes. However, there are many methodological limitations to these approaches. This research proposed a three component model of successful faking to address this, where an original response is manipulated into a strategic response, which must match a criteria target. Further, by operationalising successful faking in this manner, this research takes into account the fact that individuals may have been successful in reaching their implicitly created profile, but that this may not have matched the criteria they were instructed to fake.Participants (N=48, 22 students and 26 non-students) completed the BDI-II honestly. Participants then faked the BDI-II as if they had no, mild, moderate and severe depression, as well as completing a checklist revealing which symptoms they thought indicated each level of depression. Findings were consistent with a three component model of successful faking, where individuals effectively changed their profile to what they believed was required, however this profile differed from the criteria defined by the psychometric norms of the test.One of the foremost issues for research in this area is the inconsistent manner in which successful faking is operationalised. This research allowed successful faking to be operationalised in an objective, quantifiable manner. Using this model as a template may allow researchers better understanding of the processes involved in faking, including the role of strategies and abilities in determining the outcome of test dissimulation.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

QUT Speaker Identity Verification system for EVALITA 2009

This document outlines the system submitted by the Speech and Audio Research Laboratory at the Queensland University of Technology (QUT) for the Speaker Identity Verification: Application task of EVALITA 2009. This competitive submission consisted of a score-level fusion of three component systems; a joint-factor analysis GMM system and two SVM systems using GLDS and GMM supervector kernels. Development evaluation and post-submission results are presented in this study, demonstrating the effectiveness of this fused system approach. This study highlights the challenges associated with system calibration from limited development data and that mismatch between training and testing conditions continues to be a major source of error in speaker verification technology.

Petrology and geochemistry of the Quaternary Caldera-forming, Phonolitic Granadilla Eruption, Tenerife (Canary Islands)

The Granadilla eruption at 600 ka was one of the largest phonolitic explosive eruptions from the Las Cañadas volcano on Tenerife, producing a classical plinian eruptive sequence of a widespread pumice fall deposit overlain by an ignimbrite. The eruption resulted in a major phase of caldera collapse that probably destroyed the shallow-level magma chamber system. Granadilla pumices contain a diverse phenocryst assemblage of alkali feldspar + biotite + sodian diopside to aegirine–augite + titanomagnetite + ilmenite + nosean/haüyne + titanite + apatite; alkali feldspar is the dominant phenocryst and biotite is the main ferromagnesian phase. Kaersutite and partially resorbed plagioclase (oligoclase to sodic andesine) are present in some eruptive units, particularly in pumice erupted during the early plinian phase, and in the Granadilla ignimbrite at the top of the sequence. Associated with the kaersutite and plagioclase are small clots of microlitic plagioclase and kaersutite interpreted as quenched blebs of tephriphonolitic magma within the phonolite pumice. The Granadilla Member has previously been recognized as an example of reverse-then-normal compositional zonation, where the zonation is primarily expressed in terms of substantial variations in trace element abundances with limited major element variation (cryptic zonation). Evidence for cryptic zonation is also provided by the chemistry of the phenocryst phases, and corresponding changes in intensive parameters (e.g. T, f O2, f  H2O). Geothermometry estimates indicate that the main body of phonolite magma had a temperature gradient from 860 °C to ∼790 °C, with hotter magma (≥900 °C) tapped at the onset and terminal phases of the eruption. The reverse-then-normal chemical and thermal zonation reflects the initial tapping of a partially hybridized magma (mixing of phonolite and tephriphonolite), followed by the more sequential tapping of a zoned and relatively large body of highly evolved phonolite at a new vent and during the main plinian phase. This suggests that the different magma types within the main holding chamber could have been laterally juxtaposed, as well as in a density-stratified arrangement. Correlations between the presence of mixed phenocryst populations (i.e. presence of plagioclase and kaersutite) and coarser pumice fall layers suggest that increased eruption vigour led to the tapping of hybridized and/or less evolved magma probably from greater depths in the chamber. New oxygen isotope data for glass and mineral separates preclude syn-eruptive interaction between the vesiculating magma and hydrothermal fluids as the cause of the Sr isotope disequilibrium identified previously for the deposit. Enrichment in radiogenic Sr in the pumice glass has more likely been due to low-temperature exchange with meteoric water that was enriched in 87Sr by sea spray, which may be a common process affecting porous and glassy pyroclastic deposits on oceanic islands.

Acoustic hazard detection for pedestrians with obscured hearing

Pedestrians’ use of mp3 players or mobile phones can pose the risk of being hit by motor vehicles. We present an approach for detecting a crash risk level using the computing power and the microphone of mobile devices that can be used to alert the user in advance of an approaching vehicle so as to avoid a crash. A single feature extractor classifier is not usually able to deal with the diversity of risky acoustic scenarios. In this paper, we address the problem of detection of vehicles approaching a pedestrian by a novel, simple, non resource intensive acoustic method. The method uses a set of existing statistical tools to mine signal features. Audio features are adaptively thresholded for relevance and classified with a three component heuristic. The resulting Acoustic Hazard Detection (AHD) system has a very low false positive detection rate. The results of this study could help mobile device manufacturers to embed the presented features into future potable devices and contribute to road safety.

Selecting rainfall events for effective Water Sensitive Urban Design (WSUD) implementation

The current approach for protecting the receiving water environment from urban stormwater pollution is the adoption of structural measures commonly referred to as Water Sensitive Urban Design (WSUD). The treatment efficiency of WSUD measures closely depends on the design of the specific treatment units. As stormwater quality can be influenced by rainfall characteristics, the selection of appropriate rainfall events for treatment design is essential to ensure the effectiveness of WSUD systems. Based on extensive field investigation of four urban residential catchments and computer modelling, this paper details a technically robust approach for the selection of rainfall events for stormwater treatment design using a three-component model. The modelling outcomes indicate that selecting smaller average recurrence interval (ARI) events with high intensity-short duration as the threshold for the treatment system design is the most feasible since these events cumulatively generate a major portion of the annual pollutant load compared to the other types of rainfall events, despite producing a relatively smaller runoff volume. This implies that designs based on small and more frequent rainfall events rather than larger rainfall events would be appropriate in the context of efficiency in treatment performance, cost-effectiveness and possible savings in land area needed.