Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Modelling and predictive control techniques for building heating systems

Model predictive control (MPC) has often been referred to in literature as a potential method for more efficient control of building heating systems. Though a significant performance improvement can be achieved with an MPC strategy, the complexity introduced to the commissioning of the system is often prohibitive. Models are required which can capture the thermodynamic properties of the building with sufficient accuracy for meaningful predictions to be made. Furthermore, a large number of tuning weights may need to be determined to achieve a desired performance. For MPC to become a practicable alternative, these issues must be addressed. Acknowledging the impact of the external environment as well as the interaction of occupants on the thermal behaviour of the building, in this work, techniques have been developed for deriving building models from data in which large, unmeasured disturbances are present. A spatio-temporal filtering process was introduced to determine estimates of the disturbances from measured data, which were then incorporated with metaheuristic search techniques to derive high-order simulation models, capable of replicating the thermal dynamics of a building. While a high-order simulation model allowed for control strategies to be analysed and compared, low-order models were required for use within the MPC strategy itself. The disturbance estimation techniques were adapted for use with system-identification methods to derive such models. MPC formulations were then derived to enable a more straightforward commissioning process and implemented in a validated simulation platform. A prioritised-objective strategy was developed which allowed for the tuning parameters typically associated with an MPC cost function to be omitted from the formulation by separation of the conflicting requirements of comfort satisfaction and energy reduction within a lexicographic framework. The improved ability of the formulation to be set-up and reconfigured in faulted conditions was shown.

All-optical OFDM and distributed Raman amplification: Challenges to enable high capacities and extend reach

We review recent advances in all-optical OFDM technologies and discuss the performance of a field trial of a 2 Tbit/s Coherent WDM over 124 km with distributed Raman amplification. The results indicate that careful optimisation of the Raman pumps is essential. We also consider how all-optical OFDM systems perform favourably against energy consumption when compared with alternative coherent detection schemes. We argue that, in an energy constrained high-capacity transmission system, direct detected all-optical OFDM with 'ideal' Raman amplification is an attractive candidate for metro area datacentre interconnects with ~100 km fibre spans, with an overall energy requirement at least three times lower than coherent detection techniques.

Dilute nitride semiconductors : band structure, scattering and high field transport

The substitution of a small fraction x of nitrogen atoms, for the group V elements in conventional III-V semiconductors such as GaAs and GaSb strongly perturbs the conduction band of the host semiconductor. In this thesis we investigate the effects of nitrogen states on the band dispersion, carrier scattering and mobility of dilute nitride alloys. In the supercell model we solve the single particle Hamiltonian for a very large supercell containing randomly placed nitrogen. This model predicts a gap in the density of states of GaNxAs1−x, where this gap is filled in the Green’s function model. Therefore we develop a self-consistent Green’s function (SCGF) approach, which provides excellent agreement with supercell calculations and reveals a gap in the DOS, in contrast with the results of previous non-self-consistent Green’s function calculations. However, including the distribution of N states destroys this gap, as seen in experiment. We then examine the high field transport of carriers by solving the steadystate Boltzmann transport equation and find that it is necessary to include the full distribution of N levels in order to account for the small, low-field mobility and the absence of a negative differential velocity regime observed experimentally with increasing x. Overall the results account well for a wide range of experimental data. We also investigate the band structure, scattering and mobility of carriers by finding the poles of the SCGF, which gives lower carrier mobility for GaNxAs1−x, compared to those already calculated, in better agreement with experiments. The calculated optical absorption spectra for InyGa1−yNxAs1−x and GaNxSb1−x using the SCGF agree well with the experimental data, confirming the validity of this approach to study the band structure of these materials.

High-current inductors for high-power automotive DC-DC converters

This thesis is focused on the investigation of magnetic materials for high-power dcdc converters in hybrid and fuel cell vehicles and the development of an optimized high-power inductor for a multi-phase converter. The thesis introduces the power system architectures for hybrid and fuel cell vehicles. The requirements for power electronic converters are established and the dc-dc converter topologies of interest are introduced. A compact and efficient inductor is critical to reduce the overall cost, weight and volume of the dc-dc converter and optimize vehicle driving range and traction power. Firstly, materials suitable for a gapped CC-core inductor are analyzed and investigated. A novel inductor-design algorithm is developed and automated in order to compare and contrast the various magnetic materials over a range of frequencies and ripple ratios. The algorithm is developed for foil-wound inductors with gapped CC-cores in the low (10 kHz) to medium (30 kHz) frequency range and investigates the materials in a natural-convection-cooled environment. The practical effects of frequency, ripple, air-gap fringing, and thermal configuration are investigated next for the iron-based amorphous metal and 6.5 % silicon steel materials. A 2.5 kW converter is built to verify the optimum material selection and thermal configuration over the frequency range and ripple ratios of interest. Inductor size can increase in both of these laminated materials due to increased airgap fringing losses. Distributing the airgap is demonstrated to reduce the inductor losses and size but has practical limitations for iron-based amorphous metal cores. The effects of the manufacturing process are shown to degrade the iron-based amorphous metal multi-cut core loss. The experimental results also suggest that gap loss is not a significant consideration in these experiments. The predicted losses by the equation developed by Reuben Lee and cited by Colonel McLyman are significantly higher than the experimental results suggest. Iron-based amorphous metal has better preformance than 6.5 % silicon steel when a single cut core and natural-convection-cooling are used. Conduction cooling, rather than natural convection, can result in the highest power density inductor. The cooling for these laminated materials is very dependent on the direction of the lamination and the component mounting. Experimental results are produced showing the effects of lamination direction on the cooling path. A significant temperature reduction is demonstrated for conduction cooling versus natural-convection cooling. Iron-based amorphous metal and 6.5% silicon steel are competitive materials when conduction cooled. A novel inductor design algorithm is developed for foil-wound inductors with gapped CC-cores for conduction cooling of core and copper. Again, conduction cooling, rather than natural convection, is shown to reduce the size and weight of the inductor. The weight of the 6.5 % silicon steel inductor is reduced by around a factor of ten compared to natural-convection cooling due to the high thermal conductivity of the material. The conduction cooling algorithm is used to develop high-power custom inductors for use in a high power multi-phase boost converter. Finally, a high power digitally-controlled multi-phase boost converter system is designed and constructed to test the high-power inductors. The performance of the inductors is compared to the predictions used in the design process and very good correlation is achieved. The thesis results have been documented at IEEE APEC, PESC and IAS conferences in 2007 and at the IEEE EPE conference in 2008.

High-efficiency photovoltaics through mechanically stacked integration of solar cells based on the InP lattice constant

Solar Energy is a clean and abundant energy source that can help reduce reliance on fossil fuels around which questions still persist about their contribution to climate and long-term availability. Monolithic triple-junction solar cells are currently the state of the art photovoltaic devices with champion cell efficiencies exceeding 40%, but their ultimate efficiency is restricted by the current-matching constraint of series-connected cells. The objective of this thesis was to investigate the use of solar cells with lattice constants equal to InP in order to reduce the constraint of current matching in multi-junction solar cells. This was addressed by two approaches: Firstly, the formation of mechanically stacked solar cells (MSSC) was investigated through the addition of separate connections to individual cells that make up a multi-junction device. An electrical and optical modelling approach identified separately connected InGaAs bottom cells stacked under dual-junction GaAs based top cells as a route to high efficiency. An InGaAs solar cell was fabricated on an InP substrate with a measured 1-Sun conversion efficiency of 9.3%. A comparative study of adhesives found benzocyclobutene to be the most suitable for bonding component cells in a mechanically stacked configuration owing to its higher thermal conductivity and refractive index when compared to other candidate adhesives. A flip-chip process was developed to bond single-junction GaAs and InGaAs cells with a measured 4-terminal MSSC efficiency of 25.2% under 1-Sun conditions. Additionally, a novel InAlAs solar cell was identified, which can be used to provide an alternative to the well established GaAs solar cell. As wide bandgap InAlAs solar cells have not been extensively investigated for use in photovoltaics, single-junction cells were fabricated and their properties relevant to PV operation analysed. Minority carrier diffusion lengths in the micrometre range were extracted, confirming InAlAs as a suitable material for use in III-V solar cells, and a 1-Sun conversion efficiency of 6.6% measured for cells with 800 nm thick absorber layers. Given the cost and small diameter of commercially available InP wafers, InGaAs and InAlAs solar cells were fabricated on alternative substrates, namely GaAs. As a first demonstration the lattice constant of a GaAs substrate was graded to InP using an InxGa1-xAs metamorphic buffer layer onto which cells were grown. This was the first demonstration of an InAlAs solar cell on an alternative substrate and an initial step towards fabricating these cells on Si. The results presented offer a route to developing multi-junction solar cell devices based on the InP lattice parameter, thus extending the range of available bandgaps for high efficiency cells.

Photonic integrated circuit for the manipulation of coherent optical combs

Photonic integration has become an important research topic in research for applications in the telecommunications industry. Current optical internet infrastructure has reached capacity with current generation dense wavelength division multiplexing (DWDM) systems fully occupying the low absorption region of optical fibre from 1530 nm to 1625 nm (the C and L bands). This is both due to an increase in the number of users worldwide and existing users demanding more bandwidth. Therefore, current research is focussed on using the available telecommunication spectrum more efficiently. To this end, coherent communication systems are being developed. Advanced coherent modulation schemes can be quite complex in terms of the number and array of devices required for implementation. In order to make these systems viable both logistically and commercially, photonic integration is required. In traditional DWDM systems, arrayed waveguide gratings (AWG) are used to both multiplex and demultiplex the multi-wavelength signal involved. AWGs are used widely as they allow filtering of the many DWDM wavelengths simultaneously. However, when moving to coherent telecommunication systems such as coherent optical frequency division multiplexing (OFDM) smaller FSR ranges are required from the AWG. This increases the size of the device which is counter to the miniaturisation which integration is trying to achieve. Much work was done with active filters during the 1980s. This involved using a laser device (usually below threshold) to allow selective wavelength filtering of input signals. By using more complicated cavity geometry devices such as distributed feedback (DFB) and sampled grating distributed Bragg gratings (SG-DBR) narrowband filtering is achievable with high suppression (>30 dB) of spurious wavelengths. The active nature of the devices also means that, through carrier injection, the index can be altered resulting in tunability of the filter. Used above threshold, active filters become useful in filtering coherent combs. Through injection locking, the coherence of the filtered wavelengths with the original comb source is retained. This gives active filters potential application in coherent communication system as demultiplexers. This work will focus on the use of slotted Fabry-Pérot (SFP) semiconductor lasers as active filters. Experiments were carried out to ensure that SFP lasers were useful as tunable active filters. In all experiments in this work the SFP lasers were operated above threshold and so injection locking was the mechanic by which the filters operated. Performance of the lasers under injection locking was examined using both single wavelength and coherent comb injection. In another experiment two discrete SFP lasers were used simultaneously to demultiplex a two-line coherent comb. The relative coherence of the comb lines was retained after demultiplexing. After showing that SFP lasers could be used to successfully demultiplex coherent combs a photonic integrated circuit was designed and fabricated. This involved monolithic integration of a MMI power splitter with an array of single facet SFP lasers. This device was tested much in the same way as the discrete devices. The integrated device was used to successfully demultiplex a two line coherent comb signal whilst retaining the relative coherence between the filtered comb lines. A series of modelling systems were then employed in order to understand the resonance characteristics of the fabricated devices, and to understand their performance under injection locking. Using this information, alterations to the SFP laser designs were made which were theoretically shown to provide improved performance and suitability for use in filtering coherent comb signals.

Infant milk formula manufacture: process and compositional interactions in high dry matter wet-mixes

Infant milk formula (IMF) is fortified milk with composition based on the nutrient content in human mother's milk, 0 to 6 months postpartum. Extensive medical and clinical research has led to advances in the nutritional quality of infant formula; however, relatively few studies have focused on interactions between nutrients and the manufacturing process. The objective of this research was to investigate the impact of composition and processing parameters on physical behaviour of high dry matter (DM) IMF systems with a view to designing more sustainable manufacturing processes. The study showed that commercial IMF, with similar compositions, manufactured by different processes, had markedly different physical properties in dehydrated or reconstituted state. Commercial products made with hydrolysed protein were more heat stable compared to products made with intact protein, however, emulsion quality was compromised. Heat-induced denaturation of whey proteins resulted in increased viscosity of wet-mixes, an effect that was dependant on both whey concentration and interactions with lactose and caseins. Expanding on fundamental laboratory studies, a novel high velocity steam injection process was developed whereby high DM (60%) wet-mixes with lower denaturation/viscosity compared to conventional processes could be achieved; powders produced using this process were of similar quality to those manufactured conventionally. Hydrolysed proteins were also shown to be an effective way of reducing viscosity in heat-treated high DM wet-mixes. In particular, using a whey protein concentrate whereby β-Lactoglobulin was selectively hydrolysed, i.e., α-Lactalbumin remained intact, reduced viscosity of wet-mixes during processing while still providing good emulsification. The thesis provides new insights into interactions between nutrients and/or processing which influence physical stability of IMF both in concentrated liquid and powdered form. The outcomes of the work have applications in such areas as; increasing the DM content of spray drier feeds in order to save energy, and, controlling final powder quality.

Cost savings from relaxation of operational constraints on a power system with high wind penetration

Wind energy is predominantly a nonsynchronous generation source. Large-scale integration of wind generation with existing electricity systems, therefore, presents challenges in maintaining system frequency stability and local voltage stability. Transmission system operators have implemented system operational constraints (SOCs) in order to maintain stability with high wind generation, but imposition of these constraints results in higher operating costs. A mixed integer programming tool was used to simulate generator dispatch in order to assess the impact of various SOCs on generation costs. Interleaved day-ahead scheduling and real-time dispatch models were developed to allow accurate representation of forced outages and wind forecast errors, and were applied to the proposed Irish power system of 2020 with a wind penetration of 32%. Savings of at least 7.8% in generation costs and reductions in wind curtailment of 50% were identified when the most influential SOCs were relaxed. The results also illustrate the need to relax local SOCs together with the system-wide nonsynchronous penetration limit SOC, as savings from increasing the nonsynchronous limit beyond 70% were restricted without relaxation of local SOCs. The methodology and results allow for quantification of the costs of SOCs, allowing the optimal upgrade path for generation and transmission infrastructure to be determined.