Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Continuous production of Bi-2212 thick film on silver tape

Bi-2212 thick film on silver tapes are seen as a simple and low cost alternative to high temperature superconducting wires produced by the Powder In Thbe (PIT) technique, particularly in react and wind applications. A rig for the continuous production of Bi-2212 tapes for use in react and wind component manufacture has been developed and commissioned. The rig consists of several sections, each fully automatic, for task specific duties in the production of HTS tape. The major sections are: tape coating, sintering and annealing. High temperature superconducting tapes with engineering critical current densities of 10 kA/cm2 (77 K, self field), and lengths of up to 100 m have been produced using the rig. Properties of the finished tape are discussed and results are presented for current density versus bend radius and applied strain. Depending on tape content and thickness, irreversible strain tirrm varies between 0.04 and 0.1 %. Cyclic bending tests when applied strain does not exceed Eirrm showed negligible reduction in J c along the length of the tape.

The impact of mining and smelting activities on property values : a study of Mount Isa city, Queensland, Australia

Much publicity has been given to the problem of high levels of environmental contaminants, most notably high blood lead concentration levels among children in the city of Mount Isa because of mining and smelting activities. The health impacts from mining-related pollutants are now well documented. This includes published research being discussed in an editorial of the Medical Journal of Australia (see Munksgaard et al. 2010). On the other hand, negative impacts on property prices, although mentioned, have not been examined to date. This study rectifies this research gap. This study uses a hedonic property price approach to examine the impact of mining- and smelting-related pollution on nearby property prices. The hypothesis is that those properties closer to the lead and copper smelters have lower property (house) prices than those farther away. The results of the study show that the marginal willingness to pay to be farther from the pollution source is AUS $13 947 per kilometre within the 4 km radius selected. The study has several policy implications, which are discussed briefly. We used ordinary least squares, geographically weighted regression, spatial error and spatial autoregressive or spatial lag models for this analysis.

Power profiles of multifocal contact lenses and their interpretation

Purpose Many contact lens (CL) manufacturers produce simultaneous-image lenses in which power varies either smoothly or discontinuously with zonal radius. We present in vitro measurements of some recent CLs and discuss how power profiles might be approximated in terms of nominal distance corrections, near additions, and on-eye visual performance. Methods Fully hydrated soft, simultaneous-image CLs from four manufacturers (Air Optix AQUA, Alcon; PureVision multifocal, Bausch & Lomb; Acuvue OASYS for Presbyopia, Vistakon; Biofinity multifocal- ‘‘D’’ design, Cooper Vision) were measured with a Phase focus Lens Profiler (Phase Focus Ltd., Sheffield,UK) in a wet cell and powerswere corrected to powers in air. All lenses had zero labeled power for distance. Results Sagittal power profiles revealed that the ‘‘low’’ add PureVision and Air Optix lenses exhibit smooth (parabolic) profiles, corresponding to negative spherical aberration. The ‘‘mid’’ and ‘‘high’’ add PureVision and Air Optix lenses have biaspheric designs, leading to different rates of power change for the central and peripheral portions. All OASYS lenses display a series of concentric zones, separated by abrupt discontinuities; individual profiles can be constrained between two parabolically decreasing curves, each giving a valid description of the power changes over alternate annular zones. Biofinity lenses have constant power over the central circular region of radius 1.5 mm, followed by an annular zone where the power increases approximately linearly, the gradient increasing with the add power, and finally an outer zone showing a slow, linear increase in power with a gradient being almost independent of the add power. Conclusions The variation in power across the simultaneous-image lenses produces enhanced depth of focus. The throughfocusnature of the image, which influences the ‘‘best focus’’ (distance correction) and the reading addition, will vary with several factors, including lens centration, the wearer’s pupil diameter, and ocular aberrations, particularly spherical aberration; visual performance with some designs may show greater sensitivity to these factors.

Characterising transiting exoplanets by way of differential photometry

This paper describes a simple activity for plotting and characterising the light curve from an exoplanet transit event by way of differential photometry analysis. Using free digital imaging software, participants analyse a series of telescope images with the goal of calculating various exoplanet parameters, including its size, orbital radius and habitability. The activity has been designed for a high-school or undergraduate university level and introduces fundamental concepts in astrophysics and an understanding of the basis for exoplanetary science, the transit method and digital photometry.

Minimizing the Gibbs–Thomson effect in the low-temperature plasma synthesis of thin Si nanowires

An advanced combination of numerical models, including plasma sheath, ion- and radical-induced species creation and plasma heating effects on the surface and within a Au catalyst nanoparticle, is used to describe the catalyzed growth of Si nanowires in the sheath of a low-temperature and low-pressure plasma. These models have been used to explain the higher nanowire growth rates, low-energy barriers, much thinner Si nanowire nucleation and the less effective Gibbs–Thomson effect in reactive plasma processes, compared with those of neutral gas thermal processes. The effects of variation in the plasma sheath parameters and substrate potential on Si nanowire nucleation and growth have also been investigated. It is shown that increasing the plasma-related effects leads to decreases in the nucleation energy barrier and the critical nanoparticle radius, with the Gibbs–Thomson effect diminished, even at low temperatures. The results obtained are consistent with available experimental results and open a path toward the energy- and matter-efficient nucleation and growth of a broad range of one-dimensional quantum structures.

Non-square-well potential profile and suppression of blinking in compositionally graded Cd1−xZnxSe/CdxZn1−xSe nanocrystals

Random blinking is a major problem on the way to successful applications of semiconducting nanocrystals in optoelectronics and photonics, which until recently had neither a practical solution nor a theoretical interpretation. An experimental breakthrough has recently been made by fabricating non-blinking Cd1-xZnxSe/ZnSe graded nanocrystals [Wang et al., Nature, 2009, 459, 686]. Here, we (1) report an unequivocal and detailed theoretical investigation to understand the properties (e.g., profile) of the potential-well and the distribution of Zn content with respect to the nanocrystal radius and (2) develop a strategy to find the relationship between the photoluminescence (PL) energy peaks and the potential-well due to Zn distribution in nanocrystals. It is demonstrated that the non-square-well potential can be varied in such a way that one can indeed control the PL intensity and the energy-level difference (PL energy peaks) accurately. This implies that one can either suppress the blinking altogether, or alternatively, manipulate the PL energy peaks and intensities systematically to achieve a controlled non-random intermittent luminescence. The approach developed here is based on the ionization energy approximation and as such is generic and can be applied to any non-free-electron nanocrystals.

Effect of pupil dilation and constriction on the distribution of bit errors within the iris

Texture information in the iris image is not uniform in discriminatory information content for biometric identity verification. The bits in an iris code obtained from the image differ in their consistency from one sample to another for the same identity. In this work, errors in bit strings are systematically analysed in order to investigate the effect of light-induced and drug-induced pupil dilation and constriction on the consistency of iris texture information. The statistics of bit errors are computed for client and impostor distributions as functions of radius and angle. Under normal conditions, a V-shaped radial trend of decreasing bit errors towards the central region of the iris is obtained for client matching, and it is observed that the distribution of errors as a function of angle is uniform. When iris images are affected by pupil dilation or constriction the radial distribution of bit errors is altered. A decreasing trend from the pupil outwards is observed for constriction, whereas a more uniform trend is observed for dilation. The main increase in bit errors occurs closer to the pupil in both cases.

An observational study of conflicts between cyclists and pedestrians in the city centre

City centres have large volumes of pedestrians and motorised traffic and increases in walking and cycling could potentially lead to more pedestrians and cyclists being injured. In this study, observers recorded cyclist characteristics, number of pedestrians within 1m and 5m radius and type of conflict (none, pedestrian, vehicle) for 1,971 cyclists in 2010 and 2,551 cyclists in 2012 at six locations in the Brisbane Central Business District. Only 1.7% of cyclists were involved in conflicts with a motor vehicle or pedestrian and no collisions were observed. Increased odds of a pedestrian-cyclist conflict was associated with: male riders, riders not wearing correctly fastened helmets, riding on the footpath, higher pedestrian density (within 1m but not within 5m), morning peak and 2-4 pm (compared with 4-6 pm), two-way roads, roads with more lanes, higher speed limits, and yellow marked bicycle symbols on the road.

Is there a bone-nail specific entry point? automated fit quantification of tibial nail designs during the insertion for six different nail entry points

Intramedullary nailing is the standard fixation method for displaced diaphyseal fractures of tibia. Selection of the correct nail insertion point is important for axial alignment of bone fragments and to avoid iatrogenic fractures. However, the standard entry point (SEP) may not always optimise the bone-nail fit due to geometric variations of bones. This study aimed to investigate the optimal entry for a given bone-nail pair using the fit quantification software tool previously developed by the authors. The misfit was quantified for 20 bones with two nail designs (ETN and ETN-Proximal Bend) related to the SEP and 5 entry points which were 5 mm and 10 mm away from the SEP. The SEP was the optimal entry point for 50% of the bones used. For the remaining bones, the optimal entry point was located 5 mm away from the SEP, which improved the overall fit by 40% on average. However, entry points 10 mm away from the SEP doubled the misfit. The optimised bone-nail fit can be achieved through the SEP and within the range of a 5 mm radius, except posteriorly. The study results suggest that the optimal entry point should be selected by considering the fit during insertion and not only at the final position.

Modular design of profluorescent polymer sensors

A simple modular strategy for the synthesis of profluorescent nitroxide containing polymers is described. The incorporation of an epoxide as a pendant functionality on a polymer backbone synthesized using ATRP and subsequent nucleophilic ring-opening with sodium azide gave hydroxyl and azide functionality within a 3-bond radius. Orthogonal coupling chemistry then allowed the independent attachment of fluorophore and nitroxide groups in close proximity, giving rise to a profluorescent polymer. Validation of the viability of these materials as fluorescent sensors is demonstrated through efficient fluorescence switch-on observed when the materials are exposed to a model reductant or carbon-centred radical source.

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Traditional and geometric morphometrics detect morphological variation of lower pharyngeal jaw inCoris julis(Teleostei, Labridae)

In the present study, variation in the morphology of the lower pharyngeal element between two Sicilian populations of the rainbow wrasse Coris julis has been explored by the means of traditional morphometrics for size and geometric morphometrics for shape. Despite close geographical distance and probable high genetic flow between the populations, statistically significant differences have been found both for size and shape. In fact, one population shows a larger lower pharyngeal element that has a larger central tooth. Compared to the other population, this population also has medially enlarged lower pharyngeal jaws with a more pronounced convexity of the medial-posterior margin. The results are discussed in the light of a possible more pronounced durophagy of this population.

The IFITM5 mutation c.-14C > T results in an elongated transcript expressed in human bone; And causes varying phenotypic severity of osteogenesis imperfecta type V

Background The genetic mutation resulting in osteogenesis imperfecta (OI) type V was recently characterised as a single point mutation (c.-14C > T) in the 5' untranslated region (UTR) of IFITM5, a gene encoding a transmembrane protein with expression restricted to skeletal tissue. This mutation creates an alternative start codon and has been shown in a eukaryotic cell line to result in a longer variant of IFITM5, but its expression has not previously been demonstrated in bone from a patient with OI type V. Methods Sanger sequencing of the IFITM5 5' UTR was performed in our cohort of subjects with a clinical diagnosis of OI type V. Clinical data was collated from referring clinicians. RNA was extracted from a bone sample from one patient and Sanger sequenced to determine expression of wild-type and mutant IFITM5. Results: All nine subjects with OI type V were heterozygous for the c.-14C > T IFITM5 mutation. Clinically, there was heterogeneity in phenotype, particularly in the manifestation of bone fragility amongst subjects. Both wild-type and mutant IFITM5 mRNA transcripts were present in bone. Conclusions The c.-14C > T IFITM5 mutation does not result in an RNA-null allele but is expressed in bone. Individuals with identical mutations in IFITM5 have highly variable phenotypic expression, even within the same family.

Uniform surface growth of copper oxide nanowires in radiofrequency plasma discharge and limiting factors

The uniform growth of copper oxide nanowires on the top of copper plate has been investigated during the exposure to radiofrequency plasma discharge in respect to plasma properties and its localization. The copper samples of 10 mm radius and 1 mm in thickness were exposed to argon-oxygen plasma created at discharge power of 150 W. After 10 min, almost uniform growth of nanowires was achieved over large surface. There were significant distortions in nanowire length and shape near the edges. Based on the experimental results, we developed a theoretical model, which took into account a balance in heat released at the flow of the current to the nanowire and rejected from the nanowire. This model established a dependence of the maximal length of the nanowire at dependence on the plasma parameters, where the limiting factor for nanowire growth and distortions in distribution are ballistic effects of ions and their local fluxes. In contrast, the plasma heating by potential interactions of species has very little influence on the length and smaller deviations in flux are allowed for uniformity of growth