A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Proportionality : a valid alternative to correlation for relative data

Relative abundance data is common in the life sciences, but appreciation that it needs special analysis and interpretation is scarce. Correlation is popular as a statistical measure of pairwise association but should not be used on data that carry only relative information. Using timecourse yeast gene expression data, we show how correlation of relative abundances can lead to conclusions opposite to those drawn from absolute abundances, and that its value changes when different components are included in the analysis. Once all absolute information has been removed, only a subset of those associations will reliably endure in the remaining relative data, specifically, associations where pairs of values behave proportionally across observations. We propose a new statistic φ to describe the strength of proportionality between two variables and demonstrate how it can be straightforwardly used instead of correlation as the basis of familiar analyses and visualization methods.

Corporate-cooperative management of fisheries: A potential alternative governance structure for low value small fisheries?

While the economic and environmental benefits of fisheries management are well accepted, the costs of effective management in low value fisheries, including the research necessary to underpin such management, may be considerable relative to the total economic benefits they may generate. Co-management is often seen as a panacea in low value fisheries. Increasing fisher participation increases legitimacy of management decision in the absence of detailed scientific input. However, where only a small number of operators exist, the potential benefits of co-management are negated by the high transaction cost to the individual fishers engaging in the management process. From an economic perspective, sole ownership has been identified as the management structure which can best achieve biological and economic sustainability. Moving low value fisheries with a small number of participants to a corporate-cooperative management model may come close to achieving these sole ownership benefits, with lower transaction costs. In this paper we look at the applicability of different management models with industry involvement to low value fisheries with a small number of participants. We provide an illustration as to how a fishery could be transitioned to a corporate-cooperative management model that captures the key benefits of sole management at a low cost and is consistent with societal objectives.

Alternative education engaging Indigenous young people: Flexi schooling in Queensland

This article will discuss some of the findings from a qualitative research project that explored the connections between alternative education and Indigenous learners. This study investigated how flexi school leaders reported they were supporting Indigenous young people to remain engaged in education. The results of the survey provide demographic data focusing on Indigenous participation in this sample of flexi schools. The results revealed that a high number of Indigenous young people are participating in flexi schools within this sample. Furthermore, a high number of Indigenous staff members are working in multiple roles within these schools. The implications of these findings are twofold. First, the current Indigenous education policy environment is focused heavily on ‘Closing the Gap’, emphasising the urgent need for significant improvement of educational outcomes for Indigenous young people. The findings from this study propose that flexi schools are playing a significant role in supporting Indigenous young people to remain engaged in education, yet there remains a limited focus on this within the literature and education policy. Second, the high participation rates of Indigenous young people and staff suggest an urgent need to explore this context through research. Further research will assist in understanding the culture of the flexi school context. Research should also explore why a high number of Indigenous young people and staff members participate in this educational context and how this could influence the approach to engagement of Indigenous young people in conventional school settings.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

On food security and alternative food networks: Understanding and performing food security in the context of urban bias

This paper offers one explanation for the institutional basis of food insecurity in Australia, and argues that while alternative food networks and the food sovereignty movement perform a valuable function in building forms of social solidarity between urban consumers and rural producers, they currently make only a minor contribution to Australia’s food and nutrition security. The paper begins by identifying two key drivers of food security: household incomes (on the demand side) and nutrition-sensitive, ‘fair food’ agriculture (on the supply side). We focus on this second driver and argue that healthy populations require an agricultural sector that delivers dietary diversity via a fair and sustainable food system. In order to understand why nutrition-sensitive, fair food agriculture is not flourishing in Australia we introduce the development economics theory of urban bias. According to this theory, governments support capital intensive rather than labour intensive agriculture in order to deliver cheap food alongside the transfer of public revenues gained from rural agriculture to urban infrastructure, where the majority of the voting public resides. We chart the unfolding of the Urban Bias across the twentieth century and its consolidation through neo-liberal orthodoxy, and argue that agricultural policies do little to sustain, let alone revitalize, rural and regional Australia. We conclude that by observing food system dynamics through a re-spatialized lens, Urban Bias Theory is valuable in highlighting rural–urban socio-economic and political economy tensions, particularly regarding food system sustainability. It also sheds light on the cultural economy tensions for alternative food networks as they move beyond niche markets to simultaneously support urban food security and sustainable rural livelihoods.

Adoption of alternative habitats by a threatened, "obligate" forest-dwelling bat in a fragmented landscape

While they are among the most ecologically important animals within forest ecosystems, little is known about how bats respond to habitat loss and fragmentation. The threatened lesser short-tailed bat (Mystacina tuberculata), considered to be an obligate deep-forest species, is one of only 2 extant land mammals endemic to New Zealand; it plays a number of important roles within native forests, including pollination and seed dispersal, and rarely occurs in modified forests. We used radiotelemetry to study the movements, roosting behavior, and habitat use of M. tuberculata within a fragmented landscape comprised of 3 main habitat types: open space (harvested forest and pastoral land), native forests, and exotic pine plantations. We found that the bats had smaller home-range areas and travelled shorter nightly distances than populations investigated previously from contiguous native forest. Furthermore, M. tuberculata occupied all 3 habitat types, with native forest being preferred overall. However, individual variation in habitat selection was high, with some bats preferring exotic plantation and open space over native forest. Roosting patterns were similar to those previously observed in contiguous forest; individual bats often switched between communal and solitary roosts. Our findings indicate that M. tuberculata exhibit some degree of behavioral plasticity that allows them to adapt to different landscape mosaics and exploit alternative habitats. To our knowledge, this is the first such documentation of plasticity in habitat use for a bat species believed to be an obligate forest-dweller.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

Organic photovoltaics using thin gold film as an alternative anode to indium tin oxide

Indium Tin Oxide (ITO) is the most commonly used anode as a transparent electrode and more recently as an anode for organic photovoltaics (OPVs). However, there are significant drawbacks in using ITO which include high material costs, mechanical instability including brittleness and poor electrical properties which limit its use in low-cost flexible devices. We present initial results of poly(3-hexylthiophene): phenyl-C61-butyric acid methyl ester OPVs showing that an efficiency of 1.9% (short-circuit current 7.01 mA/cm2, open-circuit voltage 0.55 V, fill factor 0.49) can be attained using an ultra thin film of gold coated glass as the device anode. The initial I-V characteristics demonstrate that using high work function metals when the thin film is kept ultra thin can be used as a replacement to ITO due to their greater stability and better morphological control.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.

An alternative approach to describing agility in sports through establishment of a relationship between velocity and radius of curvature

Agility is an essential part of many athletic activities. Currently, agility drill duration is the sole criterion used for evaluation of agility performance. The relationship between drill duration and factors such as acceleration, deceleration and change of direction, however, has not been fully explored. This paper provides a mathematical description of the relationship between velocity and radius of curvatures in an agility drill through implementation of a power law (PL). Two groups of skilled and unskilled participants performed a cyclic forward/backward shuttle agility test. Kinematic data was recorded using motion capture system at a sampling rate of 200 Hz. The logarithmic relationship between tangential velocity and radius of curvature of participant trajectories in both groups was established using the PL. The slope of the regression line was found to be 0.26 and 0.36, for the skilled and unskilled groups, respectively. The magnitudes of regression line slope for both groups were approximately 0.3 which is close to the expected 1/3 value. Results are an indication of how the PL could be implemented in an agility drill thus opening the way for establishment of a more representative measure of agility performance instead of drill duration.