669 resultados para Mathematical-theory


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Boards of directors are key governancemechanisms in organizations and fulfill twomain tasks:monitoringmanagers and firm performance, and providing advice and access to resources. In spite of a wealth of researchmuch remains unknown about how boards attend to the two tasks. This study investigates whether organizational (firm profitability) and environmental factors (industry regulation) affect board task performance. The data combine CEOs' responses to a questionnaire, and archival data from a sample of large Italian firms. Findings show that past firm performance is negatively associatedwith board monitoring and advice tasks; greater industry regulation enhances perceived board task performance; board monitoring and advice tasks tend to reinforce each other, despite their theoretical and practical distinction.

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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.

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This research studies information systems that adapt to the context in which they are used and provides recommendations on how the design of such systems can be improved. This thesis covers the problem of context-awareness via two case studies in the insurance and transportation industries. The study highlights shortcomings in the understanding of the relationship between information systems and context. Furthermore, it presents a new, theory-informed approach to design, and provides guidance for system developers seeking to implement context-aware information systems.

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In 2010, six Threshold Learning Outcomes (TLOs) for law were developed by the Australian Learning and Teaching Council's Discipline Scholars: Law. The final of these outcomes, TLO 6, concerns self-management. This thesis examines strategies for implementing self-management in Australian legal education by first contextualising the development of TLO 6 in light of other relevant national and international developments in higher education, and secondly, analysing this learning outcome through the lens of Self-Determination Theory (SDT), an influential branch of educational psychology. It is argued that the central concept of autonomous self-regulation in SDT provides insights into factors that are relevant to law students’ capacities for long-term self-management, which is reinforced by analysis of the literature on law students’ distress. Accordingly, curriculum design that supports students’ autonomy may simultaneously promote students’ self-management capacities. The discussion of theoretical and practical perspectives on autonomy supportive curriculum design in this thesis thus illuminates potential pedagogical approaches for the implementation of TLO 6 in Australian legal curricula.

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In this thesis, three mathematical models describing the growth of solid tumour incorporating the host tissue and the immune system response are developed and investigated. The initial model describes the dynamics of the growing tumour and immune response before being extended in the second model by introducing a time-varying dendritic cell-based treatment strategy. Finally, in the third model, we present a mathematical model of a growing tumour using a hybrid cellular automata. These models can provide information to pre-experimental work to assist in designing more effective and efficient laboratory experiments related to tumour growth and interactions with the immune system and immunotherapy.

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Amonia borane (AB) has been identified as a potential candidate highcapacity hydrogen storage material. This work probes the adsorption and dissociation of AB inside and outside single-walled carbon nanotubes (SWCNTs) within the framework of density functional theory. The dissociation barriers of AB have been calculated and compared with that of the isolated AB molecule. On the basis of the present calculations, no notable improvement results from SWCNT confinement; on the contrary, the dissociation barrier slightly increases with respect to isolated AB.

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First principle calculations for a hexagonal (graphene-like) boron nitride (g-BN) monolayer sheet in the presence of a boron-atom vacancy show promising properties for capture and activation of carbon dioxide. CO2 is found to decompose to produce an oxygen molecule via an intermediate chemisorption state on the defect g-BN sheet. The three stationary states and two transition states in the reaction pathway are confirmed by minimum energy pathway search and frequency analysis. The values computed for the two energy barriers involved in this catalytic reaction after enthalpy correction indicate that the catalytic reaction should proceed readily at room temperature.

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Strong binding of isolated carbon dioxide (CO2) on aluminium nitride (AlN) single walled nanotubes is verified using two different functionals. Two optimized configurations corresponding to physisorption and chemisorption are linked by a low energy barrier, such that the chemisorbed state is accessible and thermodynamically favored at low temperatures. In contrast, N2 is found only to form a physisorbed complex with the AlN nanotube, suggesting the potential application of aluminium nitride based materials for CO2 fixation. The effect of nanotube diameter on gas adsorption properties is also discussed. The diameter is found to have an important effect on the chemisorption of CO2, but has little effect on the physisorption of either CO2 or N2.

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The adsorption of carbon dioxide and nitrogen molecules on aluminum nitride (AlN) nanostructures has been explored using first-principle computational methods. Optimized configurations corresponding to physisorption and, subsequentially, chemisorption of CO2 are identified, in contrast to N2, for which only a physisorption structure is found. Transition-state searches imply a low energy barrier between the physisorption and chemisorption states for CO2 such that the latter is accessible and thermodynamically favored at room temperature. The effective binding energy of the optimized chemisorption structure is apparently larger than those for other CO2 adsorptive materials, suggesting the potential for application of aluminum nitride nanostructures for carbon dioxide capture and storage.

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An ab initio density functional theory (DFT) study with correction for dispersive interactions was performed to study the adsorption of N2 and CO2 inside an (8, 8) single-walled carbon nanotube. We find that the approach of combining DFT and van der Waals correction is very effective for describing the long-range interaction between N2/CO2 and the carbon nanotube (CNT). Surprisingly, exohedral doping of an Fe atom onto the CNT surface will only affect the adsorption energy of the quadrupolar CO2 molecule inside the CNT (20–30%), and not that of molecular N2. Our results suggest the feasibility of enhancement of CO2/N2 separation in CNT-based membranes by using exohedral doping of metal atoms.

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Recent work [S. Chaudhuri, J.T. Muckerman, J. Phys. Chem. B 109 (2005) 6952] reported that two Ti-substituted atoms on an Al(0 0 1) surface can form a catalytically active site for the dissociation of H2, but the diffusion barrier of atomic H away from Ti site is as high as 1.57 eV. By using ab initio density functional calculations, we found that two hydrogen molecules can dissociate on isolated-Ti atom doped Al(0 0 1) surface with small activation barriers (0.21 and 0.235 eV for first and second H2, respectively). Additionally, the diffusion barrier of atomic H away from Ti site is also moderate (0.47 eV). These results contribute further towards understanding the improved kinetics observed in recycling of hydrogen with Ti-doped NaAlH4.

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Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

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The Design Science Research Roadmap (DSR-Roadmap) [1] aims to give detailed methodological guidance to novice researchers in Information Systems (IS) DSR. Focus group evaluation, one phase of the overall study, of the evolving DSR-Roadmap revealed that a key difficulty faced by both novice and expert researchers in DSR, is abstracting design theory from design. This paper explores the extension of the DSR-Roadmap by employing IS deep structure ontology (BWW [2-4]) as a lens on IS design to firstly yield generalisable design theory, specifically 'IS Design Theory' (ISDT) elements [5]. Consideration is next given to the value of BWW in the application of the design theory by practitioners. Results of mapping BWW constructs to ISDT elements suggest that the BWW is promising as a common language between design researchers and practitioners, facilitating both design theory and design implementation

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Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem. Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.