A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations

In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using tensor product cubic spline basis functions defined on a background rectangular (interpolation) mesh, which leads to high spatial accuracy and straightforward implementation, and establishes a solid base for extending the computational framework to three-dimensional problems. A semi-implicit time-stepping method is employed to transform the nonlinear partial differential equation into a linear boundary value problem. A key finding of our study is that the newly proposed mesh-free finite volume method based on circular control volumes reduces to the collocation method as the radius limits to zero. Both methods produce a large constrained least-squares problem that must be solved at each time step in the advancement of the solution. We have found that regularization yields a relatively well-conditioned system that can be solved accurately using QR factorization. An extensive numerical investigation is performed to illustrate the effectiveness of the present methods, including the application of the new method to a coupled system of time-fractional partial differential equations having different fractional indices in different (irregularly shaped) regions of the solution domain

Control Theory: The Double Pendulum Inverted on a Cart

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to the DPIC system to derive a Linear Quadratic Regulator (LQR). Two different LQR controllers are then applied to the full nonlinear DPIC system, which is concurrently modeled in MATLAB. Also, an in-depth look is taken at the Riccati equation and its solutions. Finally, results from various MATLAB simulations are shown

The enigma of facial asymmetry:is there a gender specific pattern of facedness?

Although facial symmetry correlates with facial attractiveness, human faces are often far from symmetrical with one side frequently being larger than the other (Kowner, 1998). Smith (2000) reported that male and female faces were asymmetrical in opposite directions, with males having a larger area on the left side compared to the right side, and females having a larger right side compared to the left side. The present study attempted to replicate and extend this finding. Two databases of facial images from Stirling and St Andrews Universities, consisting of 180 and 122 faces respectively, and a third set of 62 faces collected at Abertay University, were used to examine Smith's findings. Smith's unique method of calculating the size of each hemiface was applied to each set. For the Stirling and St Andrews sets a computer program did this automatically and for the Abertay set it was done manually. No significant overall effect of gender on facial area asymmetry was found. However, the St Andrews sample demonstrated a similar effect to that found by Smith, with females having a significantly larger mean area of right hemiface and males having a larger left hemiface. In addition, for the Abertay faces handedness had a significant effect on facial asymmetry with right-handers having a larger left side of the face. These findings give limited support for Smith's results but also suggest that finding such an asymmetry may depend on some as yet unidentified factors inherent in some methods of image collection

Effect of Relative Marker Movement on the Calculation of the Foot Torsion Axis Using a Combined Cardan Angle and Helical Axis Approach

The two main movements occurring between the forefoot and rearfoot segment of a human foot are flexion at the metatarsophalangeal joints and torsion in the midfoot. The location of the torsion axis within the foot is currently unknown. The purpose of this study was to develop a method based on Cardan angles and the finite helical axis approach to calculate the torsion axis without the effect of flexion. As the finite helical axis method is susceptible to error due to noise with small helical rotations, a minimal amount of rotation was defined in order to accurately determine the torsion axis location. Using simulation, the location of the axis based on data containing noise was compared to the axis location of data without noise with a one-sample t-test and Fisher's combined probability score. When using only data with helical rotation of seven degrees or more, the location of the torsion axis based on the data with noise was within 0.2 mm of the reference location. Therefore, the proposed method allowed an accurate calculation of the foot torsion axis location

The properties and tunable nature of electrochemically-grown peptide-based hydrogels at single microelectrodes

Microelectrodes possess enhanced mass transport properties which make them desirable over macroelectrodes in point-of-care electrochemical biosensing platforms. Due to their scale, microelectrode biosensors also face a heightened receptiveness to biofouling, often characterised by the nonspecific binding of large molecules and cells to the sensing layer or electrode surface. This ultimately prevents the biosensor from providing an accurate measure of a chemical target. Anti-fouling, semi-permeable membranes are employed to prevent biofouling at point-of-care biosensors. Recently, peptide-based supramolecular hydrogels have been considered as anti-fouling membranes which can encapsulate and immobilise sensing layers. A pH shift generated by the electrochemical oxidation of hydroquinone triggers the self-assembly of dissolved gelator molecules local to the electrode surface, and the peptide-based gelator molecules aggregate into fibre-like structures that entangle to form the gel in these localised acidic regions. This thesis first explores the extent to which Carb-Ala hydrogels can be tuned at single 25 μm diameter Pt disc microelectrodes under potentiostatic control. Altering the time and potential applied has allowed for the production of gels with different sizes and densities using the same stock gelator solution, identified by pairing optical microscopy (both in situ and ex situ) and electrochemical impedance spectroscopy techniques. In doing so, a dynamic process between gel assembly and disassembly has been demonstrated: the gels first undergo a loss in density before a collapse in structure, characterised by a gradual increase in transparency and a gradual increase in the diffusion coefficients of a ferro/ferricyanide redox probe. This process was first observed during continuous gel growth, likely caused by a shift in the dominance of gelator deprotonation and network disassembly (driven by bulk pH 8 gelator solution flux) over self-assembly (driven by proton generation via hydroquinone oxidation). The gels underwent a similar loss in density followed by structure collapse in buffered pH 4.3 and unbuffered pH 0 solutions, though the rate of gel loss was decreased in the lower pH conditions. The phenomenon was also shown not be exclusive to Carb-Ala, as electrochemical gels of a second peptide-gelator BrAV also underwent these changes on a similar timescale. These observations suggested that gel instability might be driven by a concentration gradient of weakly-bound gelator at the electrode surface and the bulk gelator-less solutions. Lastly, a simple use-case for these gels as enzyme immobilising layers in a 1st generation enzymatic biosensor is presented. To avoid enzyme leaching with the breakdown of gels, electropolymerisation of Carb-Ala post-gelation was utilised as a way of stabilising the preformed, tuned microscale gels. The resulting GOx/Carb-Ala polymer-functionalised glucose biosensors were capable of producing progressively greater signals in the presence of increasing concentrations of glucose (due to the electrochemical oxidation of the H2O2 produced by the enzymes), and the calibration curves of each electrode displayed characteristic Michaelis-Menten kinetics. The sensors possessed a biologically relevant linear calibration range of 0-4 mM, a maximum sensitivity of 189 ± 9 μM mM-1 cm2, a LOD of 0.33 mM, and a t1/2 of up to 44 days at 37 °C

Safety margins and adaptive capacity of vegetation to climate change

Vegetation is composed of many individual species whose climatic tolerances can be integrated into spatial analyses of climate change risk. Here, we quantify climate change risk to vegetation at a continental scale by calculating the safety margins for warming and drying (i.e., tolerance to projected change in temperature and precipitation respectively) across plants sharing 100km × 100km grid cells (locations). These safety margins measure how much warmer, or drier, a location could become before its ‘typical’ species exceeds its observed climatic limit. We also analyse the potential adaptive capacity of vegetation to temperature and precipitation change (i.e., likelihood of in situ persistence) using median precipitation and temperature breadth across all species in each location. 47% of vegetation across Australia is potentially at risk from increases in mean annual temperature (MAT) by 2070, with tropical regions most vulnerable. Vegetation at high risk from climate change often also exhibited low adaptive capacity. By contrast, 2% of the continent is at risk from reductions in annual precipitation by 2070. Risk from precipitation change was isolated to the southwest of Western Australia where both the safety margin for drier conditions in the typical species is low, and substantial reductions in MAP are projected

A giant new trimerellide brachiopod from the Wenlock (Early Silurian) of New South Wales, Australia

Keteiodoros bellense n.gen. and n.sp. is a remarkably large trimerellide brachiopod from the Wenlock Dripstone Formation, southeast of Wellington, central New South Wales. The probable articulatory mechanism is unusual for trimerellides. It apparently involved both flattened sections of the lateral commissures which acted as pivots for opening and closing the shell, and a large and strongly modified articulating plate (which partly envelopes a robust dorsal umbo) articulating with the pseudointerarea at the posterior end of the ventral platform. The heavy dorsal umbo probably acted as a counterbalance to the anterior part of the valve; the diductor muscles were apparently attached to the umbo at the sides of the articulating plate, and to the anterior end of the ventral platform. The trimerellides occur in presumed life position in nearly mono specific beds which are interpreted as having formed in a quiet inshore shallow subtidal area on a sloping shelf, protected by coral biostromes but periodically disrupted by storm action. They are considered to represent a low-diversity quietwater Benthic Assemblage 2 community

A survey of leaf phosphorus fractions and leaf economic traits among 12 co-occurring woody species on phosphorus-impoverished soils

Background and Aims: The leaf economic spectrum (LES) is related to dry mass and nutrient investments towards photosynthetic processes and leaf structures, and to the duration of returns on those investments (leaf lifespan, LL). Phosphorus (P) is a key limiting nutrient for plant growth, yet it is unclear how the allocation of leaf P among different functions is coordinated with the LES. We addressed this question among 12 evergreen woody species co-occurring on P-impoverished soils in south-eastern Australia. Methods: Leaf ‘economic’ traits, including LL, leaf mass per area (LMA), light-saturated net photosynthetic rate per mass (Amass), dark respiration rate, P concentration ([Ptotal]), nitrogen concentration, and P resorption, were measured for three pioneer and nine non-pioneer species. Leaf P was separated into five functional fractions: orthophosphate P (Pi), metabolite P (PM), nucleic acid P (PN), lipid P (PL), and residual P (PR; phosphorylated proteins and unidentified compounds that contain P). Results: LL was negatively correlated with Amass and positively correlated with LMA, representing the LES. Pioneers occurred towards the short-LL end of the spectrum and exhibited higher [Ptotal] than non-pioneer species, primarily associated with higher concentrations of Pi, PN and PL. There were no significant correlations between leaf P fractions and LL or LMA, while Amass was positively correlated with the concentration of PR. Conclusions: Allocation of leaf P to different fractions varied substantially among species. This variation was partially associated with the LES, which may provide a mechanism underlying co-occurrence of species with different ecological strategies under P limitation

Palliative care needs in patients hospitalized with heart failure (PCHF) study: rationale and design

Abstract Aims The primary aim of this study is to provide data to inform the design of a randomized controlled clinical trial (RCT) of a palliative care (PC) intervention in heart failure (HF). We will identify an appropriate study population with a high prevalence of PC needs defined using quantifiable measures. We will also identify which components a specific and targeted PC intervention in HF should include and attempt to define the most relevant trial outcomes. Methods An unselected, prospective, near-consecutive, cohort of patients admitted to hospital with acute decompensated HF will be enrolled over a 2-year period. All potential participants will be screened using B-type natriuretic peptide and echocardiography, and all those enrolled will be extensively characterized in terms of their HF status, comorbidity, and PC needs. Quantitative assessment of PC needs will include evaluation of general and disease-specific quality of life, mood, symptom burden, caregiver burden, and end of life care. Inpatient assessments will be performed and after discharge outpatient assessments will be carried out every 4 months for up to 2.5 years. Participants will be followed up for a minimum of 1 year for hospital admissions, and place and cause of death. Methods for identifying patients with HF with PC needs will be evaluated, and estimates of healthcare utilisation performed. Conclusion By assessing the prevalence of these needs, describing how these needs change over time, and evaluating how best PC needs can be identified, we will provide the foundation for designing an RCT of a PC intervention in HF

Assessing the vulnerability of plant functional trait strategies to climate change

Aim: Our ability to understand how species may respond to changing climate conditions is hampered by a lack of high-quality data on the adaptive capacity of species. Plant functional traits are linked to many aspects of species life history and adaptation to environment, with different combinations of trait values reflecting alternate strategies for adapting to varied conditions. If the realized climate limits of species can be partially explained by plant functional trait combinations, then a new approach of using trait combinations to predict the expected climate limits of species trait combinations may offer considerable benefits. Location: Australia. Time period: Current and future. Methods: Using trait data for leaf size, seed mass and plant height for 6,747 Australian native species from 27 plant families, we model the expected climate limits of trait combinations and use future climate scenarios to estimate climate change impacts based on plant functional trait strategies. Results: Functional trait combinations were a significant predictor of species climate niche metrics with potentially meaningful relationships with two rainfall variables (R2 =.36 &.45) and three temperature variables (R2 =.21,.28,.30). Using this method, the proportion of species exposed to conditions across their range that are beyond the expected climate limits of their trait strategies will increase under climate change. Main conclusions: Our new approach, called trait strategy vulnerability, includes three new metrics. For example, the climate change vulnerability (CCV) metric identified a small but important proportion of species (4.3%) that will on average be exposed to conditions beyond their expected limits for summer temperature in the future. These potentially vulnerable species could be high priority targets for deeper assessment of adaptive capacity at the genomic or physiological level. Our methods can be applied to any suite of co-occurring plants globally