A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Early-mid Cretaceous tectonic evolution of eastern Gondwana : from silicic LIP magmatism to continental rupture

The Early–mid Cretaceous marks the confluence of three major continental-scale events in eastern Gondwana: (1) the emplacement of a Silicic Large Igneous Province (LIP) near the continental margin; (2) the volcaniclastic fill, transgression and regression of a major epicontinental seaway developed over at least a quarter of the Australian continent; and (3) epeirogenic uplift, exhumation and continental rupturing culminating in the opening of the Tasman Basin c. 84 Ma. The Whitsunday Silicic LIP event had widespread impact, producing both substantial extrusive volumes of dominantly silicic pyroclastic material and coeval first-cycle volcanogenic sediment that accumulated within many eastern Australian sedimentary basins, and principally in the Great Australian Basin system (>2 Mkm3 combined volume). The final pulse of volcanism and volcanogenic sedimentation at c. 105–95 Ma coincided with epicontinental seaway regression, which shows a lack of correspondence with the global sea-level curve, and alternatively records a wider, continental-scale effect of volcanism and rift tectonism. Widespread igneous underplating related to this LIP event is evident from high paleogeothermal gradients and regional hydrothermal fluid flow detectable in the shallow crust and over a broad region. Enhanced CO2 fluxing through sedimentary basins also records indirectly, large-scale, LIP-related mafic underplating. A discrete episode of rapid crustal cooling and exhumation began c. 100–90 Ma along the length of the eastern Australian margin, related to an enhanced phase of continental rifting that was largely amagmatic, and probably a switch from wide–more narrow rift modes. Along-margin variations in detachment fault architecture produced narrow (SE Australia) and wide continental margins with marginal, submerged continental plateaux (NE Australia). Long-lived NE-trending cross-orogen lineaments controlled the switch from narrow to wide continental margin geometries.

New insights into magmatism and changing rift styles in the evolution of the Gulf of California

The Gulf of California (GoC) has been an important focus site for understanding the spatial and temporal evolution of rifts, with recent studies concluding: 1) rapid crustal rupturing within 10 Myrs; 2) surprisingly abrupt variations in rifting style and magmatism with apparently wide magma-poor and narrow, magmatic rift segments; and 3) that high sedimentation rates may promote switching from wide to narrow rift modes or thermally blanket the crust to enhance rift magmatism. Critical to these conclusions is the onset of rifting at~12 Ma following the cessation of subduction. New field-based volcanostratigraphic and geochronologic studies along the southeastern GoC margin reveal Early Miocene (~25-18 Ma) bimodal volcanism in wide rifting mode (~400 km width), followed by a mid-Miocene (~18-12 Ma) phase of dominantly intermediate composition magmatism in and around the nascent GoC with lavas/domes often emplaced into actively subsiding basins, but contemporaneous with bimodal volcanism regionally. Flat-lying intraplate basaltic lava fields emplaced ~12-10 Ma along the GoC east coast abut tilted blocks of ~20 Ma ignimbrites onshore, and also occur offshore. The reduction in crustal thickness from ~55 to 20 km along the eastern GoC edge must have been largely achieved by 12 Ma. Extension has demonstrably began earlier than previously thought, downplaying rapid rifting and any thermal effects from <6 Ma sedimentation. New age data from onshore indicate significant structurally controlled corridors of magmatism during 18-12 Ma extension in apparently magma-poor rift segments, and this magmatism temporally coincides with the switch from wide to narrow rifting.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Cometary evolution : clues on physical properties from chondritic interplanetary dust particles

The degree of diversity or similarity detected in comets depends primarily on the lifetimes of the individual cometary nuclei at the time of analysis. It is inherent in our understanding of cometary orbital dynamics and the seminal model of comet origins that cometary evolution is the natural order of events in our Solar System. Thus, predictions of cometary behaviour in terms of bulk physical, mineralogical or chemical parameters should contain an appreciation of temporal variation(s). Previously, Rietmeijer and Mackinnon [1987] developed mineralogical bases for the chemical evolution of cometary nuclei primarily with regard to the predominantly silicate fraction of comet nuclei. We suggested that alteration of solids in cometary nuclei should be expected and that indications of likely reactants and products can be derived from judicious comparison with terrestrial diagenetic environments which include hydrocryogenic and low-temperature aqueous alterations. In a further development of this concept, Rietmeijer [1988] provides indirect evidence for the formation of sulfides and oxides in comet nuclei. Furthermore, Rietmeijer [1988] noted that timescales for hydrocryogenic and low-temperature reactions involving liquid water are probably adequate for relatively mature comets, e.g. P/comet Halley. In this paper, we will address the evolution of comet nuclei physical parameters such as solid particle grain size, porosity and density. In natural environments, chemical evolution (e.g. mineral reactions) is often accompanied by changes in physical properties. These concurrent changes are well-documented in the terrestrial geological literature, especially in studies of sediment diagenesis and we suggest that similar basic principles apply within the upper few meters of active comet nuclei. The database for prediction of comet nuclei physical parameters is, in principle, the same as used for the proposition of chemical evolution. We use detailed mineralogical studies of chondritic interplanetary dust particles (IDPS) as a guide to the likely constitution of mature comets traversing the inner Solar System. While there is, as yet, no direct proof that a specific sub-group or type of chondritic IDP is derived from a specific comet, it is clear that these particles are extraterrestrial in origin and that a certain portion of the interplanetary flux received by the Earth is cometary in origin. Two chondritic porous (CP) IDPS, sample numbers W701OA2 and W7029CI, from the Johnson Space Center Cosmic Dust Collection have been selected for this study of putative cometary physical parameters. This particular type of particle is considered a likely candidate for a cometary origin on the basis of mineralogy, bulk composition and morphology. While many IDPs have been subjected to intensive study over the past decade, we can develop a physical parameter model on only these two CP IDPs because few others have been studied in sufficient detail.

Evolution and innovation in guardianship laws: Assisted decision-making

Guardianship laws in most Western societies provide decision-making mechanisms for adults with impaired capacity. Since the inception of these laws, the principle of autonomy and recognition of human rights for those coming within guardianship regimes has gained prominence. A new legal model has emerged, which seeks to incorporate ‘assisted decision-making’ models into guardianship laws. Such models legally recognise that an adult’s capacity may be maintained through assistance or support provided by another person, and provide formal recognition of the person in that ‘assisting’ role. This article situates this latest legal innovation within a historical context, examining the social and legal evolution of guardianship laws and determining whether modern assisted decision-making models remain consistent with guardianship reform thus far. It identifies and critically analyses the different assisted decision-making models which exist internationally. Finally, it discusses a number of conceptual, legal and practical concerns that remain unresolved. These issues require serious consideration before assisted decisionmaking models are adopted in guardianship regimes in Australia.

Genomic evidence for the parallel evolution of coastal forms in the Senecio lautus complex

Instances of parallel ecotypic divergence where adaptation to similar conditions repeatedly cause similar phenotypic changes in closely related organisms are useful for studying the role of ecological selection in speciation. Here we used a combination of traditional and next generation genotyping techniques to test for the parallel divergence of plants from the Senecio lautus complex, a phenotypically variable groundsel that has adapted to disparate environments in the South Pacific. Phylogenetic analysis of a broad selection of Senecio species showed that members of the S. lautus complex form a distinct lineage that has diversified recently in Australasia. An inspection of thousands of polymorphisms in the genome of 27 natural populations from the S. lautus complex in Australia revealed a signal of strong genetic structure independent of habitat and phenotype. Additionally, genetic differentiation between populations was correlated with the geographical distance separating them, and the genetic diversity of populations strongly depended on geographical location. Importantly, coastal forms appeared in several independent phylogenetic clades, a pattern that is consistent with the parallel evolution of these forms. Analyses of the patterns of genomic differentiation between populations further revealed that adjacent populations displayed greater genomic heterogeneity than allopatric populations and are differentiated according to variation in soil composition. These results are consistent with a process of parallel ecotypic divergence in face of gene flow.

The evolution and biogeography of the austral horse fly tribe Scionini (Diptera: Tabanidae: Pangoniinae) inferred from multiple mitochondrial and nuclear genes

Phylogenetic relationships within the Tabanidae are largely unknown, despite their considerable medical and ecological importance. The first robust phylogenetic hypothesis for the horse fly tribe Scionini is provided, completing the systematic placement of all tribes in the subfamily Pangoniinae. The Scionini consists of seven mostly southern hemisphere genera distributed in Australia, New Guinea, New Zealand and South America. A 5757. bp alignment of 6 genes, including mitochondrial (COI and COII), ribosomal (28S) and nuclear (AATS and CAD regions 1, 3 and 4) genes, was analysed for 176 taxa using both Bayesian and maximum likelihood approaches. Results indicate the Scionini are strongly monophyletic, with the exclusion of the only northern hemisphere genus Goniops. The South American genera Fidena, Pityocera and Scione were strongly monophyletic, corresponding to current morphology-based classification schemes. The most widespread genus Scaptia was paraphyletic and formed nine strongly supported monophyletic clades, each corresponding to either the current subgenera or several previously synonymised genera that should be formally resurrected. Molecular results also reveal a newly recognised genus endemic to New Zealand, formerly placed within Scaptia. Divergence time estimation was employed to assess the global biogeographical patterns in the Pangoniinae. These analyses demonstrated that the Scionini are a typical Gondwanan group whose diversification was influenced by the fragmentation of that ancient land mass. Furthermore, results indicate that the Scionini most likely originated in Australia and subsequently radiated to New Zealand and South American by both long distance dispersal and vicariance. The phylogenetic framework of the Scionini provided herein will be valuable for taxonomic revisions of the Tabanidae.

Timing, origin and emplacement dynamics of mass flows offshore of SE Montserrat in the last 110 ka : implications for landslide and tsunami hazards, eruption history, and volcanic island evolution

Mass flows on volcanic islands generated by volcanic lava dome collapse and by larger-volume flank collapse can be highly dangerous locally and may generate tsunamis that threaten a wider area. It is therefore important to understand their frequency, emplacement dynamics, and relationship to volcanic eruption cycles. The best record of mass flow on volcanic islands may be found offshore, where most material is deposited and where intervening hemipelagic sediment aids dating. Here we analyze what is arguably the most comprehensive sediment core data set collected offshore from a volcanic island. The cores are located southeast of Montserrat, on which the Soufriere Hills volcano has been erupting since 1995. The cores provide a record of mass flow events during the last 110 thousand years. Older mass flow deposits differ significantly from those generated by the repeated lava dome collapses observed since 1995. The oldest mass flow deposit originated through collapse of the basaltic South Soufriere Hills at 103-110 ka, some 20-30 ka after eruptions formed this volcanic center. A ∼1.8 km3 blocky debris avalanche deposit that extends from a chute in the island shelf records a particularly deep-seated failure. It likely formed from a collapse of almost equal amounts of volcanic edifice and coeval carbonate shelf, emplacing a mixed bioclastic-andesitic turbidite in a complex series of stages. This study illustrates how volcanic island growth and collapse involved extensive, large-volume submarine mass flows with highly variable composition. Runout turbidites indicate that mass flows are emplaced either in multiple stages or as single events.

Evolution of lure response in tephritid fruit flies : phytochemicals as drivers of sexual selection

The males of many Bactrocera species (Diptera: Tephritidae) respond strongly and positively to a small number of plant-derived chemicals (=male lures). Males that have imbibed the lures commonly have a mating advantage over unfed males, but no female benefits have been demonstrated for females mating with lure-fed males. It has been hypothesized that the strong lure response is a case of runaway selection, where males receive direct benefits and females receive indirect benefits via 'sexy sons', or a case of sensory bias where females have a lower threshold response to lures. To test these hypotheses we studied the effects of lure feeding on male mating, remating and longevity; while for females that had mated with lure-fed males we recorded mating refractoriness, fecundity, egg viability and longevity. We used Bactrocera tryoni as our test animal and as lures the naturally occurring zingerone and chemically related, but synthetic chemical cuelure. Feeding on lures provided direct male benefits in greater mating success and increased multiple mating. For the first time, we recorded direct female effects: increased fecundity and reduced remating receptivity. Egg viability did not differ in females mated with lure-fed or unfed males. The life span of males and females exposed to lures was reduced. These results reveal direct, current-generation fitness benefits for both males and females, although the male benefits appear greater. We discuss that while lure response is indeed likely to be a sexual selection trait, there is no need to invoke runaway selection to explain its evolution.

Nonlinear actuator fault detection for small-scale UAS

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating corresponding velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.

A nonlinear position controller for maritime operations of Rotary-wing UAVs

This paper presents a disturbance attenuation controller for horizontal position stabilization for hover and automatic landings of a Rotary-wing Unmanned Aerial Vehicle (RUAV) operating in rough seas. Based on a helicopter model representing aerodynamics during the landing phase, a nonlinear state feedback H-infinity controller is designed to achieve rapid horizontal position tracking in a gusty environment. The resultant control variables are further treated in consideration of practical constraints (flapping dynamics, servo dynamics and time lag effect) for implementation purpose. The high-fidelity closed-loop simulation using parameters of the Vario helicopter verifies performance of the proposed position controller. It not only increases the disturbance attenuation capability of the RUAV, but also enables rapid position response when gusts occur. Comparative studies show that the H-infinity controller exhibits great performance improvement and can be applied to ship/RUAV landing systems.