Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Measuring and monitoring soil organic carbon stocks in agricultural lands for climate mitigation

Policies that encourage greenhouse-gas emitters to mitigate emissions through terrestrial carbon (C) offsets – C sequestration in soils or biomass – will promote practices that reduce erosion and build soil fertility, while fostering adaptation to climate change, agricultural development, and rehabilitation of degraded soils. However none of these benefits will be possible until changes in C stocks can be documented accurately and cost-effectively. This is particularly challenging when dealing with changes in soil organic C (SOC) stocks. Precise methods for measuring C in soil samples are well established, but spatial variability in the factors that determine SOC stocks makes it difficult to document change. Widespread interest in the benefits of SOC sequestration has brought this issue to the fore in the development of US and international climate policy. Here, we review the challenges to documenting changes in SOC stocks, how policy decisions influence offset documentation requirements, and the benefits and drawbacks of different sampling strategies and extrapolation methods.

The role of soil characteristics on temperature sensitivity of soil organic matter

The uncertainty associated with how projected climate change will affect global C cycling could have a large impact on predictions of soil C stocks. The purpose of our study was to determine how various soil decomposition and chemistry characteristics relate to soil organic matter (SOM) temperature sensitivity. We accomplished this objective using long-term soil incubations at three temperatures (15, 25, and 35°C) and pyrolysis molecular beam mass spectrometry (py-MBMS) on 12 soils from 6 sites along a mean annual temperature (MAT) gradient (2–25.6°C). The Q10 values calculated from the CO2 respired during a long-term incubation using the Q10-q method showed decomposition of the more resistant fraction to be more temperature sensitive with a Q10-q of 1.95 ± 0.08 for the labile fraction and a Q10-q of 3.33 ± 0.04 for the more resistant fraction. We compared the fit of soil respiration data using a two-pool model (active and slow) with first-order kinetics with a three-pool model and found that the two and three-pool models statistically fit the data equally well. The three-pool model changed the size and rate constant for the more resistant pool. The size of the active pool in these soils, calculated using the two-pool model, increased with incubation temperature and ranged from 0.1 to 14.0% of initial soil organic C. Sites with an intermediate MAT and lowest C/N ratio had the largest active pool. Pyrolysis molecular beam mass spectrometry showed declines in carbohydrates with conversion from grassland to wheat cultivation and a greater amount of protected carbohydrates in allophanic soils which may have lead to differences found between the total amount of CO2 respired, the size of the active pool, and the Q10-q values of the soils.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Properties of lignin and poly(hydroxybutyrate) blends

The Queensland University of Technology (QUT) allows the presentation of a thesis for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of Seven published/submitted papers and one poster presentation, of which five have been published and the other two are under review. This project is financially supported by the QUTPRA Grant. The twenty-first century started with the resurrection of lignocellulosic biomass as a potential substitute for petrochemicals. Petrochemicals, which enjoyed the sustainable economic growth during the past century, have begun to reach or have reached their peak. The world energy situation is complicated by political uncertainty and by the environmental impact associated with petrochemical import and usage. In particular, greenhouse gasses and toxic emissions produced by petrochemicals have been implicated as a significant cause of climate changes. Lignocellulosic biomass (e.g. sugarcane biomass and bagasse), which potentially enjoys a more abundant, widely distributed, and cost-effective resource base, can play an indispensible role in the paradigm transition from fossil-based to carbohydrate-based economy. Poly(3-hydroxybutyrate), PHB has attracted much commercial interest as a plastic and biodegradable material because some its physical properties are similar to those of polypropylene (PP), even though the two polymers have quite different chemical structures. PHB exhibits a high degree of crystallinity, has a high melting point of approximately 180°C, and most importantly, unlike PP, PHB is rapidly biodegradable. Two major factors which currently inhibit the widespread use of PHB are its high cost and poor mechanical properties. The production costs of PHB are significantly higher than for plastics produced from petrochemical resources (e.g. PP costs $US1 kg-1, whereas PHB costs $US8 kg-1), and its stiff and brittle nature makes processing difficult and impedes its ability to handle high impact. Lignin, together with cellulose and hemicellulose, are the three main components of every lignocellulosic biomass. It is a natural polymer occurring in the plant cell wall. Lignin, after cellulose, is the most abundant polymer in nature. It is extracted mainly as a by-product in the pulp and paper industry. Although, traditionally lignin is burnt in industry for energy, it has a lot of value-add properties. Lignin, which to date has not been exploited, is an amorphous polymer with hydrophobic behaviour. These make it a good candidate for blending with PHB and technically, blending can be a viable solution for price and reduction and enhance production properties. Theoretically, lignin and PHB affect the physiochemical properties of each other when they become miscible in a composite. A comprehensive study on structural, thermal, rheological and environmental properties of lignin/PHB blends together with neat lignin and PHB is the targeted scope of this thesis. An introduction to this research, including a description of the research problem, a literature review and an account of the research progress linking the research papers is presented in Chapter 1. In this research, lignin was obtained from bagasse through extraction with sodium hydroxide. A novel two-step pH precipitation procedure was used to recover soda lignin with the purity of 96.3 wt% from the black liquor (i.e. the spent sodium hydroxide solution). The precipitation process is presented in Chapter 2. A sequential solvent extraction process was used to fractionate the soda lignin into three fractions. These fractions, together with the soda lignin, were characterised to determine elemental composition, purity, carbohydrate content, molecular weight, and functional group content. The thermal properties of the lignins were also determined. The results are presented and discussed in Chapter 2. On the basis of the type and quantity of functional groups, attempts were made to identify potential applications for each of the individual lignins. As an addendum to the general section on the development of composite materials of lignin, which includes Chapters 1 and 2, studies on the kinetics of bagasse thermal degradation are presented in Appendix 1. The work showed that distinct stages of mass losses depend on residual sucrose. As the development of value-added products from lignin will improve the economics of cellulosic ethanol, a review on lignin applications, which included lignin/PHB composites, is presented in Appendix 2. Chapters 3, 4 and 5 are dedicated to investigations of the properties of soda lignin/PHB composites. Chapter 3 reports on the thermal stability and miscibility of the blends. Although the addition of soda lignin shifts the onset of PHB decomposition to lower temperatures, the lignin/PHB blends are thermally more stable over a wider temperature range. The results from the thermal study also indicated that blends containing up to 40 wt% soda lignin were miscible. The Tg data for these blends fitted nicely to the Gordon-Taylor and Kwei models. Fourier transform infrared spectroscopy (FT-IR) evaluation showed that the miscibility of the blends was because of specific hydrogen bonding (and similar interactions) between reactive phenolic hydroxyl groups of lignin and the carbonyl group of PHB. The thermophysical and rheological properties of soda lignin/PHB blends are presented in Chapter 4. In this chapter, the kinetics of thermal degradation of the blends is studied using thermogravimetric analysis (TGA). This preliminary investigation is limited to the processing temperature of blend manufacturing. Of significance in the study, is the drop in the apparent energy of activation, Ea from 112 kJmol-1 for pure PHB to half that value for blends. This means that the addition of lignin to PHB reduces the thermal stability of PHB, and that the comparative reduced weight loss observed in the TGA data is associated with the slower rate of lignin degradation in the composite. The Tg of PHB, as well as its melting temperature, melting enthalpy, crystallinity and melting point decrease with increase in lignin content. Results from the rheological investigation showed that at low lignin content (.30 wt%), lignin acts as a plasticiser for PHB, while at high lignin content it acts as a filler. Chapter 5 is dedicated to the environmental study of soda lignin/PHB blends. The biodegradability of lignin/PHB blends is compared to that of PHB using the standard soil burial test. To obtain acceptable biodegradation data, samples were buried for 12 months under controlled conditions. Gravimetric analysis, TGA, optical microscopy, scanning electron microscopy (SEM), differential scanning calorimetry (DSC), FT-IR, and X-ray photoelectron spectroscopy (XPS) were used in the study. The results clearly demonstrated that lignin retards the biodegradation of PHB, and that the miscible blends were more resistant to degradation compared to the immiscible blends. To obtain an understanding between the structure of lignin and the properties of the blends, a methanol-soluble lignin, which contains 3× less phenolic hydroxyl group that its parent soda lignin used in preparing blends for the work reported in Chapters 3 and 4, was blended with PHB and the properties of the blends investigated. The results are reported in Chapter 6. At up to 40 wt% methanolsoluble lignin, the experimental data fitted the Gordon-Taylor and Kwei models, similar to the results obtained soda lignin-based blends. However, the values obtained for the interactive parameters for the methanol-soluble lignin blends were slightly lower than the blends obtained with soda lignin indicating weaker association between methanol-soluble lignin and PHB. FT-IR data confirmed that hydrogen bonding is the main interactive force between the reactive functional groups of lignin and the carbonyl group of PHB. In summary, the structural differences existing between the two lignins did not manifest itself in the properties of their blends.

Loss of chance in medical negligence claims now a lost cause?

The question whether the loss of chance of a better medical outcome in cases of medical negligence should be recognised as actionable damage is ‘a question which has divided courts and commentators throughout the common law world.’ In April 2010, the High Court handed down its anticipated decision in the case of Tabet (by her Tutor Sheiban) v Gett (2010) 240 CLR 537. The issue considered by the court was whether the appellant could claim in negligence for the loss of a chance of a better medical outcome. This issue had not been considered by the High Court previously, the most relevant cases being Rufo v Hosking (2004) 61 NSWLR 678 and Gavalas v Singh (2001) 3 VLR 404. Claiming for a loss of chance in a personal injury action raises questions as to recognised damage and causation, and the members of the High Court considered both of these.

The Tension between a constructed self and universal reason in considerations of elective death

Review of Coping with Choices to Die, by C. G. Prado. Cambridge: Cambridge University Press, 2011.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

Controls on iron in soils and soil waters of a forested, coastal catchment in subtropical Australia

Soluble organic matter derived from exotic Pinus vegetation forms stronger complexes with iron (Fe) than the soluble organic matter derived from most native Australian species. This has lead to concern about the environmental impacts related to the establishment of extensive exotic Pinus plantations in coastal southeast Queensland, Australia. It has been suggested that the Pinus plantations may enhance the solubility of Fe in soils by increasing the amount of organically complexed Fe. While this remains inconclusive, the environmental impacts of an increased flux of dissolved, organically complexed Fe from soils to the fluvial system and then to sensitive coastal ecosystems are potentially damaging. Previous work investigated a small number of samples, was largely laboratory based and had limited application to field conditions. These assessments lacked field-based studies, including the comparison of the soil water chemistry of sites associated with Pinus vegetation and undisturbed native vegetation. In addition, the main controls on the distribution and mobilisation of Fe in soils of this subtropical coastal region have not been determined. This information is required in order to better understand the relative significance of any Pinus enhanced solubility of Fe. The main aim of this thesis is to determine the controls on Fe distribution and mobilisation in soils and soil waters of a representative coastal catchment in southeast Queensland (Poona Creek catchment, Fraser Coast) and to test the effect of Pinus vegetation on the solubility and speciation of Fe. The thesis is structured around three individual papers. The first paper identifies the main processes responsible for the distribution and mobilisation of labile Fe in the study area and takes a catchment scale approach. Physicochemical attributes of 120 soil samples distributed throughout the catchment are analysed, and a new multivariate data analysis approach (Kohonen’s self organising maps) is used to identify the conditions associated with high labile Fe. The second paper establishes whether Fe nodules play a major role as an iron source in the catchment, by determining the genetic mechanism responsible for their formation. The nodules are a major pool of Fe in much of the region and previous studies have implied that they may be involved in redox-controlled mobilisation and redistribution of Fe. This is achieved by combining a detailed study of a ferric soil profile (morphology, mineralogy and micromorphology) with the distribution of Fe nodules on a catchment scale. The third component of the thesis tests whether the concentration and speciation of Fe in soil solutions from Pinus plantations differs significantly from native vegetation soil solutions. Microlysimeters are employed to collect unaltered, in situ soil water samples. The redox speciation of Fe is determined spectrophotometrically and the interaction between Fe and dissolved organic matter (DOM) is modelled with the Stockholm Humic Model. The thesis provides a better understanding of the controls on the distribution, concentration and speciation of Fe in the soils and soil waters of southeast Queensland. Reductive dissolution is the main mechanism by which mobilisation of Fe occurs in the study area. Labile Fe concentrations are low overall, particularly in the sandy soils of the coastal plain. However, high labile Fe is common in seasonally waterlogged and clay-rich soils which are exposed to fluctuating redox conditions and in organic-rich soils adjacent to streams. Clay-rich soils are most common in the upper parts of the catchment. Fe nodules were shown to have a negligible role in the redistribution of dissolved iron in the catchment. They are formed by the erosion, colluvial transport and chemical weathering of iron-rich sandstones. The ferric horizons, in which nodules are commonly concentrated, subsequently form through differential biological mixing of the soil. Whereas dissolution/ reprecipitation of the Fe cements is an important component of nodule formation, mobilised Fe reprecipitates locally. Dissolved Fe in the soil waters is almost entirely in the ferrous form. Vegetation type does not affect the concentration and speciation of Fe in soil waters, although Pinus DOM has greater acidic functional group site densities than DOM from native vegetation. Iron concentrations are highest in the high DOM soil waters collected from sandy podosols, where they are controlled by redox potential. Iron concentrations are low in soil solutions from clay and iron oxide rich soils, in spite of similar redox potentials. This is related to stronger sorption to the reactive clay and iron oxide mineral surfaces in these soils, which reduces the amount of DOM available for microbial metabolisation and reductive dissolution of Fe. Modelling suggests that Pinus DOM can significantly increase the amount of truly dissolved ferric iron remaining in solution in oxidising conditions. Thus, inputs of ferrous iron together with Pinus DOM to surface waters may reduce precipitation of hydrous ferric oxides and increase the flux of dissolved iron out of the catchment. Such inputs are most likely from the lower catchment, where podosols planted with Pinus are most widely distributed. Significant outcomes other than the main aims were also achieved. It is shown that mobilisation of Fe in podosols can occur as dissolved Fe(II) rather than as Fe(III)-organic complexes. This has implications for the large body of work which assumes that Fe(II) plays a minor role. Also, the first paper demonstrates that a data analysis approach based on Kohonen’s self organising maps can facilitate the interpretation of complex datasets and can help identify geochemical processes operating on a catchment scale.

Psycho-markers of weight loss. The roles of TFEQ Disinhibition and Restraint in exercise-induced weight management

Eating behaviour traits, namely Disinhibition and Restraint, have the potential to exert an effect on food intake and energy balance. The effectiveness of exercise as a method of weight management could be influenced by these traits. Fifty eight overweight and obese participants completed 12-weeks of supervised exercise. Each participant was prescribed supervised exercise based on an expenditure of 500 kcal/session, 5 d/week for 12-weeks. Following 12-weeks of exercise there was a significant reduction in mean body weight (-3.26 ± 3.63 kg), fat mass (FM: -3.26 ± 2.64 kg), BMI (-1.16 ± 1.17 kg/m2)and waist circumference (WC: -5.0 ± 3.23 cm). Regression analyses revealed a higher baseline Disinhibition score was associated with a greater reduction in BMI and WC, while Internal Disinhibition was associated with a larger decrease in weight, %FM and WC. Neither baseline Restraint or Hunger were associated with any of the anthropometric markers at baseline or after 12-weeks. Furthermore, after 12-weeks of exercise, a decrease in Disinhibition and increase in Restraint were associated with a greater reduction in WC, whereas only Restraint was associated with a decrease in weight. Post-hoc analysis of the sub-factors revealed a decrease in External Disinhibition and increase in Flexible Restraint were associated with weight loss. However, an increase in Rigid Restraint was associated with a reduction in %FM and WC. These findings suggest that exercise-induced weight loss is more marked in individuals with a high level of Disinhibition. These data demonstrate the important roles that Disinhibition and Restraint play in the relationship between exercise and energy balance.