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.

Evolution of epitaxial graphene layers on 3C SiC/Si (111) as a function of annealing temperature in UHV

The growth of graphene on SiC/Si substrates is an appealing alternative to the growth on bulk SiC for cost reduction and to better integrate the material with Si based electronic devices. In this paper, we present a complete in-situ study of the growth of epitaxial graphene on 3C SiC (111)/Si (111) substrates via high temperature annealing (ranging from 1125˚C to 1375˚C) in ultra high vacuum (UHV). The quality and number of graphene layers have been thoroughly investigated by using x-ray photoelectron spectroscopy (XPS), while the surface characterization have been studied by scanning tunnelling microscopy (STM). Ex-situ Raman spectroscopy measurements confirm our findings, which demonstrate the exponential dependence of the number of graphene layer from the annealing temperature.

Ross River virus evolution : implications for vaccine development

Ross River virus is a mosquito-borne alphavirus that causes approximately 5000 cases of epidemic polyarthritis in Australia each year and has direct medical-associated costs of approximately US$15 million annually. While mosquito control programs are able, at best, to contain rather than prevent this disease, natural infection with Ross River virus confers lifelong protection against subsequent clinical infection. A killed-virus vaccine has been developed, which is in Phase III clinical trials. Analyses of intra-host genetic diversity and of long-term evolutionary changes in Ross River virus populations suggest that antigenic variation is unlikely to pose a threat to the efficacy of this vaccine.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

Mathematical models of bubble evolution in a Hele-Shaw Cell

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.