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.

Achieving high reliability for ambiguity resolutions with multiple GNSS constellations

Global Navigation Satellite Systems (GNSS)-based observation systems can provide high precision positioning and navigation solutions in real time, in the order of subcentimetre if we make use of carrier phase measurements in the differential mode and deal with all the bias and noise terms well. However, these carrier phase measurements are ambiguous due to unknown, integer numbers of cycles. One key challenge in the differential carrier phase mode is to fix the integer ambiguities correctly. On the other hand, in the safety of life or liability-critical applications, such as for vehicle safety positioning and aviation, not only is high accuracy required, but also the reliability requirement is important. This PhD research studies to achieve high reliability for ambiguity resolution (AR) in a multi-GNSS environment. GNSS ambiguity estimation and validation problems are the focus of the research effort. Particularly, we study the case of multiple constellations that include initial to full operations of foreseeable Galileo, GLONASS and Compass and QZSS navigation systems from next few years to the end of the decade. Since real observation data is only available from GPS and GLONASS systems, the simulation method named Virtual Galileo Constellation (VGC) is applied to generate observational data from another constellation in the data analysis. In addition, both full ambiguity resolution (FAR) and partial ambiguity resolution (PAR) algorithms are used in processing single and dual constellation data. Firstly, a brief overview of related work on AR methods and reliability theory is given. Next, a modified inverse integer Cholesky decorrelation method and its performance on AR are presented. Subsequently, a new measure of decorrelation performance called orthogonality defect is introduced and compared with other measures. Furthermore, a new AR scheme considering the ambiguity validation requirement in the control of the search space size is proposed to improve the search efficiency. With respect to the reliability of AR, we also discuss the computation of the ambiguity success rate (ASR) and confirm that the success rate computed with the integer bootstrapping method is quite a sharp approximation to the actual integer least-squares (ILS) method success rate. The advantages of multi-GNSS constellations are examined in terms of the PAR technique involving the predefined ASR. Finally, a novel satellite selection algorithm for reliable ambiguity resolution called SARA is developed. In summary, the study demonstrats that when the ASR is close to one, the reliability of AR can be guaranteed and the ambiguity validation is effective. The work then focuses on new strategies to improve the ASR, including a partial ambiguity resolution procedure with a predefined success rate and a novel satellite selection strategy with a high success rate. The proposed strategies bring significant benefits of multi-GNSS signals to real-time high precision and high reliability positioning services.

Organisational change stressor and nursing job satisfaction : the mediating effect of coping strategies

Aim To examine the mediating effect of coping strategies on the consequences of nursing and non-nursing (administrative) stressors on the job satisfaction of nurses during change management. Background Organisational change can result in an increase in nursing and nonnursing- related stressors, which can have a negative impact on the job satisfaction of nurses employed in health-care organisations. Method Matched data were collected in 2009 via an online survey at two timepoints (six months apart). Results Partial least squares path analysis revealed a significant causal relationship between Time 1 administrative and role stressors and an increase in nursing-specific stressors in Time 2. A significant relationship was also identified between job-specific nursing stressors and the adoption of effective coping strategies to deal with increased levels of change-induced stress and strain and the likelihood of reporting higher levels of job satisfaction in Time 2. Conclusions The effectiveness of coping strategies is critical in helping nurses to deal with the negative consequences of organisational change. Implications for nursing management This study shows that there is a causal relationship between change, non-nursing stressors and job satisfaction. Senior management should implement strategies aimed at reducing nursing and nonnursing stress during change in order to enhance the job satisfaction of nurses. Keywords: Australia, change management, job satisfaction, nursing and non-nursing stressors, public and non-profit sector

Generalised gamma bidding model

A generalised gamma bidding model is presented, which incorporates many previous models. The log likelihood equations are provided. Using a new method of testing, variants of the model are fitted to some real data for construction contract auctions to find the best fitting models for groupings of bidders. The results are examined for simplifying assumptions, including all those in the main literature. These indicate no one model to be best for all datasets. However, some models do appear to perform significantly better than others and it is suggested that future research would benefit from a closer examination of these.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.

Adaptive estimation of HMM transition probabilities

This paper presents new schemes for recursive estimation of the state transition probabilities for hidden Markov models (HMM's) via extended least squares (ELS) and recursive state prediction error (RSPE) methods. Local convergence analysis for the proposed RSPE algorithm is shown using the ordinary differential equation (ODE) approach developed for the more familiar recursive output prediction error (RPE) methods. The presented scheme converges and is relatively well conditioned compared with the ...

Spectrophotometric analysis of phenols, which involves a hemin-graphene hybrid nanoparticles with peroxidase-like activity

Phenols are well known noxious compounds, which are often found in various water sources. A novel analytical method has been researched and developed based on the properties of hemin–graphene hybrid nanosheets (H–GNs). These nanosheets were synthesized using a wet-chemical method, and they have peroxidase-like activity. Also, in the presence of H2O2, the nanosheets are efficient catalysts for the oxidation of the substrate, 4-aminoantipine (4-AP), and the phenols. The products of such an oxidation reaction are the colored quinone-imines (benzodiazepines). Importantly, these products enabled the differentiation of the three common phenols – pyrocatechol, resorcin and hydroquinone, with the use of a novel, spectroscopic method, which was developed for the simultaneous determination of the above three analytes. This spectroscopic method produced linear calibrations for the pyrocatechol (0.4–4.0 mg L−1), resorcin (0.2–2.0 mg L−1) and hydroquinone (0.8–8.0 mg L−1) analytes. In addition, kinetic and spectral data, obtained from the formation of the colored benzodiazepines, were used to establish multi-variate calibrations for the prediction of the three phenol analytes found in various kinds of water; partial least squares (PLS), principal component regression (PCR) and artificial neural network (ANN) models were used and the PLS model performed best.

Competitive interactions of anti-carcinogens with serum albumin: A spectroscopic study of bendamustine and dexamethasone with the aid of chemometrics

Interactions between the anti-carcinogens, bendamustine (BDM) and dexamethasone (DXM), with bovine serum albumin (BSA) were investigated with the use of fluorescence and UV–vis spectroscopies under pseudo-physiological conditions (Tris–HCl buffer, pH 7.4). The static mechanism was responsible for the fluorescence quenching during the interactions; the binding formation constant of the BSA–BDM complex and the binding number were 5.14 × 105 L mol−1 and 1.0, respectively. Spectroscopic studies for the formation of BDM–BSA complex were interpreted with the use of multivariate curve resolution – alternating least squares (MCR–ALS), which supported the complex formation. The BSA samples treated with site markers (warfarin – site I and ibuprofen – site II) were reacted separately with BDM and DXM; while both anti-carcinogens bound to site I, the binding constants suggested that DXM formed a more stable complex. Relative concentration profiles and the fluorescence spectra associated with BDM, DXM and BSA, were recovered simultaneously from the full fluorescence excitation–emission data with the use of the parallel factor analysis (PARAFAC) method. The results confirmed that on addition of DXM to the BDM–BSA complex, the BDM was replaced and the DXM–BSA complex formed; free BDM was released. This finding may have consequences for the transport of these drugs during any anti-cancer treatment.

Simultaneous voltammetric determination of four triazine herbicides in water samples with the aid of chemometrics

A novel differential pulse voltammetry (DPV) method was developed for the simultaneous analysis of herbicides in water. A mixture of four herbicides, atrazine, simazine, propazine and terbuthylazine was analyzed simultaneously and the complex, overlapping DPV voltammograms were resolved by several chemometrics methods such as partial least squares (PLS), principal component regression (PCR) and principal component–artificial networks (PC–ANN). The complex profiles of the voltammograms collected from a synthetic set of samples were best resolved with the use of the PC–ANN method, and the best predictions of the concentrations of the analytes were obtained with the PC-ANN model (%RPET = 6.1 and average %Recovery = 99.0). The new method was also used for analysis of real samples, and the obtained results were compared well with those from the GC-MS technique. Such conclusions suggest that the novel method is a viable alternative to the other commonly used methods such as GC, HPLC and GC-MS.

Differentiation of cultivars of flos chrysanthemum with the use of high-performance liquid chromatography fingerprints and chemometrics

Flos Chrysanthemum is a generic name for a particular group of edible plants, which also have medicinal properties. There are, in fact, twenty to thirty different cultivars, which are commonly used in beverages and for medicinal purposes. In this work, four Flos Chrysanthemum cultivars, Hangju, Taiju, Gongju, and Boju, were collected and chromatographic fingerprints were used to distinguish and assess these cultivars for quality control purposes. Chromatography fingerprints contain chemical information but also often have baseline drifts and peak shifts, which complicate data processing, and adaptive iteratively reweighted, penalized least squares, and correlation optimized warping were applied to correct the fingerprint peaks. The adjusted data were submitted to unsupervised and supervised pattern recognition methods. Principal component analysis was used to qualitatively differentiate the Flos Chrysanthemum cultivars. Partial least squares, continuum power regression, and K-nearest neighbors were used to predict the unknown samples. Finally, the elliptic joint confidence region method was used to evaluate the prediction ability of these models. The partial least squares and continuum power regression methods were shown to best represent the experimental results.

Combining HPLC-DAD and ICP-MS data for improved analysis of complex samples: Classification of the root samples from Cortex moutan

A combined data matrix consisting of high performance liquid chromatography–diode array detector (HPLC–DAD) and inductively coupled plasma-mass spectrometry (ICP-MS) measurements of samples from the plant roots of the Cortex moutan (CM), produced much better classification and prediction results in comparison with those obtained from either of the individual data sets. The HPLC peaks (organic components) of the CM samples, and the ICP-MS measurements (trace metal elements) were investigated with the use of principal component analysis (PCA) and the linear discriminant analysis (LDA) methods of data analysis; essentially, qualitative results suggested that discrimination of the CM samples from three different provinces was possible with the combined matrix producing best results. Another three methods, K-nearest neighbor (KNN), back-propagation artificial neural network (BP-ANN) and least squares support vector machines (LS-SVM) were applied for the classification and prediction of the samples. Again, the combined data matrix analyzed by the KNN method produced best results (100% correct; prediction set data). Additionally, multiple linear regression (MLR) was utilized to explore any relationship between the organic constituents and the metal elements of the CM samples; the extracted linear regression equations showed that the essential metals as well as some metallic pollutants were related to the organic compounds on the basis of their concentrations

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.