Gravel filters are potentially a low cost, low maintenance water treatment solution. They require no mechanical or electrical parts and can operate without the addition of chemicals or the need for close supervision. As such, they are an appropriate technology for treating road runoff as a component of Sustainable urban Drainage Systems (SuDS) and as an initial stage of drinking water treatment in rural areas. However, the processes by which pollutant particles are removed in gravel filters are poorly understood and practical experience shows that many filters fail long before their expected design life is reached. For this reason gravel filters are little used for drinking water treatment and, when they are incorporated into SuDS, their removal efficiency and maintenance requirements are unpredictable. The aim of this thesis was to better understand particle removal processes and the implications for gravel filter design. This was achieved through a combination of lab-based experiments and numerical modelling. • The change in conservative tracer transport characteristics with pollutant particle accumulation was assessed through column experiments. • The spatial heterogeneity of particle accumulation was measured by collecting 3D data with magnetic resonance imaging (MRI). Multiple scans of filters allowed the temporal evolution of particle accumulation to be assessed. A method for processing the raw MRI data to yield the change in 3D pore geometry was developed, assessed and applied. • A simple method for extracting and comparing pore network characteristics at different stages of particle accumulation was applied to the MRI derived geometry. • Direct modelling of the 3D MRI pore geometry with the open source software OpenFOAM allowed correlation of flow velocities with particle accumulation at each point in the pore network. Lagrangian particle tracking was used to simulate the transport of a conservative tracer through the filter. Key findings were that spatial heterogeneity in particle accumulation was influenced by both initial pore geometry and the temporal evolution of the pore network with accumulation. This was attributed to the formation of high velocity preferential flow paths that were evident in both the 3D MRI data and the numerical model of that data. Pore networks exhibited a decrease in connectivity with accumulation and this was mirrored by a decrease in the volume of the filter that was accessible to a conservative tracer. Conclusions of this thesis are that MRI is a useful tool for non-invasively assessing the spatial variability of clogging in gravel filters and, when combined with numerical modelling of the pore geometry, for establishing the link between pore velocity and particle removal. The formation of preferential flow paths is detrimental to the pollutant removal efficiency of a filter and could explain why many filters fail to produce good quality effluent well before their physical pollutant storage capacity is reached.

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Thesis (MMed)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Background Occult blood loss from the gastrointestinal tract (GIT), causing iron deficiency often with anaemia, can be diagnostically and therapeutically challenging. This is because the endoscopic and radiologic tests may be negative due to the slow, chronic and intermittent nature of the gastrointestinal bleeding, making timing key in detection and localisation of the bleed. These limitations can be approached using two different radioactive isotopes. Firstly, we tested the sensitivity of extending Cr-51 RBC for 21 days relative to 5 days to detect GIT bleeding and its use to optimise timing of a Tc-99m RBC study for GIT blood loss localisation. Finally, we tested if the information provided by the Tc-99m RBC study aided gastroenterologic intervention for anatomical localisation of a lesion. Method In this retrospective review, after obtaining institutional and ethics committee approval, records of patients referred for evaluation of possible GIT blood loss were reviewed. In each; daily appearance of radiochromium in stool was measured in the whole body counter. In those cases exceeding 50 ml/day, a technetium-99m (Tc-99m) localization study was performed. These studies were correlated with clinical findings. Results A total of 59 Cr-51 RBC studies were carried out in 36 females and 21 males (n = 57). In 32 (54%) the radiochromium results were positive with 75% of the bleeding incidences occurring after 5 days of stool collection. Of 17 cases in whom Tc-99m RBC imaging studies were performed, 14 (82%) were positive with specific anatomical sites successfully defined in twelve. In all patients with blood loss of >100 ml/24h, Tc-99m RBC were positive and localised. Ten of the 17 Tc-99m RBC studies were further investigated and half diagnosed with small-bowel angiodysplasia. Conclusion This sequential twin isotope method is practical in revealing otherwise silent intestinal haemorrhage. Although it has good patient acceptability and clinical as well as diagnostic utility in management, further studies are required to clearly establish a cut-off level of blood loss for performing imaging studies and the impact of the findings on the overall patient management. / AFRIKAANSE OPSOMMING: Agtergrond Die evaluasie van okkulte bloedverlies uit die gastro-intestinale kanaal (GIT), met gevolglike ystertekort anemie, kan diagnosties en terapeuties uitdagend wees. Dit is omdat endoskopiese en radiologiese ondersoeke negatief mag wees as gevolg van die stadige, chroniese en intermitterende aard van die gastro-intestinale bloeding, wat die presiese tydstip van opsporing en lokalisering van die bloeding krities belangrik maak. Hierdie beperkings kan aangespreek word deur twee verskillende radioaktiewe isotope te gebruik. Eerstens is die sensitiwiteit van die verlenging van die Cr-51 RBS studie tot 21 dae in plaas van 5 dae om die GIT bloeding op te spoor, getoets, asook die gebruik daarvan om die optimale tyd vir ‘n Tc-99m RBS studie om die GIT bloedverlies te lokaliseer, vas te stel. Laastens is getoets of die inligting van die Tc-99m RBS studie wel bygedra het tot die gastroenterologiese ingreep om die letsel anatomies te lokaliseer. Metode Na institusionele en etiese komitee toestemming is inligting van pasiënte wat vir die evaluering van ‘n moontlike GI bloedverlies verwys is, in hierdie retrospektiewe oorsig nagegaan. Die daaglikse voorkoms van radioaktiewe chroom in stoelgangmonsters is in ‘n heelliggaamteller gemeet. In gevalle waar dit 50 ml/dag oorskry het, is ‘n tegnesium 99m (Tc 99m) studie gedoen. Hierdie studies is met die kliniese bevindinge gekorreleer. Resultate ‘n Totaal van 59 Cr-51 RBS studies is in 36 vroue en 21 mans (n = 57) gedoen. Die gemerkte chroomstudies was positief in 32 (54%), met 75% van die bloedings wat meer as 5 dae na versameling van die stoelgang plaasgevind het. In veertien (82%) van die 17 gevalle waar Tc-99m RBS studies gedoen is, was die studies positief. Spesifieke anatomiese gebiede van bloeding kon in 12 hiervan suksesvol bevestig word. Tc-99m RBS studies was positief in al die pasiënte met ‘n bloedverlies van >100 ml/24h, en kon gelokaliseer word. Tien van die 17 Tc-99m RBS studies is verder ondersoek en die helfte daarvan gediagnoseer met dunderm angiodisplasie. Gevolgtrekking Die opeenvolgende twee isotoopmetode om andersins asimptomatiese dermbloeding op te spoor, is prakties uitvoerbaar. Alhoewel die studies goed deur pasiënte aanvaar is, en ook van kliniese en diagnostiese waarde in die hantering van die pasiënte is, is verdere studies nodig om die afsnypunt vir die hoeveelheid bloedverlies om beeldingstudies uit te voer, sonder twyfel vas te stel, asook om die impak van die bevindings op ‘n groter pasiëntpopulasie vas te stel.

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Condensed matter physics is a rapidly evolving field of research enriched with the synthesis of new materials exhibiting a bewildering variety of phenomena and advances in experimental techniques. Over the years, discoveries and innovations in electronic systems have emphasized the crucial role played by correlations among electrons behind many of the observed unusual properties and have posed serious challenges to the physics community by exposing the lack of well-controlled theoretical methods to study the class of materials known as strongly correlated electronic systems. In these systems, known theoretical techniques typically fail to capture the essential features of the many-body ground state and finite temperature properties of the systems as typical electronic interaction energies are of order of or larger than the kinetic energies. The study of strongly correlated electronic systems went through a revolution in the 1980s and 1990s after the discovery of superconductivity inorganic compounds, in heavy fermion systems and ultimately in copper oxides, referred to as cuprates, by Bednorz and Muller. In particular, the pursuit of understanding the mysterious origin of superconductivity in the cuprates and other associated strange phenomena has fascinated the condensed matter community over last two and half decades leading to most of the important unsolved, and probably interconnected, problems of quantum condensed matter physics such as the metal-insulator transition in low dimensions breakdown of Fermi liquid theory, the origin and behavior of unconventional superconductivity, quantum critical points, electronic in homogeneities and localization in interacting systems. This thesis is devoted to the study of some of the aspects of high-temperature superconductivity and associated phenomena in cuprates. In what follows, I give an overview of the organization of the thesis in to different chapters and their contents. For setting up the stage, in Chapter 1, I give a brief account of some of the remarkable phenomena and properties observed in strongly correlated electronic matter and their salient features, that continue to draw much attention and excitement in current times. The peculiarity of the state of affairs in these systems is emphasized and motivated in the background of the paradigmatic Landau Fermi liquid theory and Hubbard model, the minimal model that is expected to capture the quintessence of electronic strong correlation. In Chapter 2, starting with a brief historical account of the discovery of superconductivity in cuprates, the crystal structure of these materials, their chemical realities and basic electronic details are reviewed. This is followed by a survey of the phase diagram of cuprates, doped with, say, x number of holes per copper site, and a plethora of experimental findings that constitute the high-c puzzle. Characteristics of various observed phases, such as the superconducting, pseudo gap and strange metal phases, are discussed on the basis off acts accumulated through various experimental probes, e.g. nuclear magnetic resonance(NMR), neutron scattering, specific heat, transport and optical conductivity measurements as well as photo emission, tunnelling and Raman spectroscopies. As elucidated, these experiments point toward the need for an unconventional mechanism of superconductivity in cuprates and, more so, for the description of the rather abnormal high-temperature normal state that is realized above the superconducting transition temperature c. Keeping in mind the fact that there is no consensus even about the minimal microscopic electronic model, I review two models, namely the three band model and the t - J model; various approximate treatments of these models have dominated the theoretical developments in this field. A large number of theoretical pictures have been proposed based on different microscopic, semi-microscopic and phenomenological approaches in the past two decades for explaining the genesis of the observed strange phenomena in high-c cuprates. I include brief discussions on only a few of them while citing relevant references. As mentioned above, a variety of approximate microscopic theories, based on both strong and weak coupling approaches, as well as numerical techniques have been tried to understand the cuprate phase diagram and capture the aspects of strong correlations in-built in Hubbard and t -J models. On the other hand, in conventional superconductors and, in general, for the study of phase transitions, phenomenological Ginzburg-Landau(GL) functionals written down from very general symmetry grounds have provided useful description for a variety of systems. Specially, Ginzburg-Landau theory has been proven to be complementary to the BCS theory for attacking a plethora of situations in superconductors, e.g., in homogeneities, structures of an isolated vortex and the vortex lattice etc. The GL functional has found wide applicability for the study of vortex matter in high-c superconductors as well. Inspired by the success of this type of phenomenological route, we propose and develop in Chapter 3 an approach, analogous in spirit to that of Ginzburg and Landau, for the superconducting and pseudogap phases of cuprates. We encompass a large number of well known phenomenologies of cuprate superconductivity in the form of a low-energy effective lattice functional of complex spin-singlet pair amplitudes with magnitude Δm and phase m, i.e. m =Δm exp(i m), that resides on the Cu-Cubonds(indexed by m)of the CuO2 planes of cuprates. The functional respects general symmetry requirements, e.g. the -wave symmetry of the superconducting order parameter as found in experiments. The assumptions and the specific physical picture behind such an approach as well as the key empirical inputs that go into it are discussed in this chapter. We calculate the superconducting transition temperature c and the average magnitude of the local pair amplitude, Δ= (Δm), using single-site mean-field theory for the model. We show that this approximation leads to general features of the doping-temperature(x - T )phase diagram in agreement with experiment. In particular, we find a phase coherent superconducting state with d-wave symmetry below a parabolic Tc (x) dome and a phase incoherent state with a perceptible local gap that persists up to a temperature around which can be thought of as a measure of the pseudogap temperature scale T* . Further, effects of thermal fluctuations beyond the mean-field level are captured via Monte Carlo(MC) simulations of the model for a finite two-dimensional (2D) lattice. We exhibit results for Tc obtained from MC simulations as well as that estimated in a cluster mean field approximation. Based on our picture we remark on contrasting scenarios proposed for the doping dependence of the pseudogap temperature. Chapter 4 describes fluctuation phenomena related to pairing degrees of freedom and manifestations of these effects in various quantities of interest, e.g. superfluid density, specific heat etc., at finite temperature. Fluctuation effects have been studied in detail in superconductors over the years and pursued mainly using either the conventional GL functional or the BCS-framework at a microscopic level. However, the picture, in which the pseudogap phase is viewed as one consisting of bond-pairs with a d-wave symmetry correlation length growing as T approaches Tc, implies fluctuation phenomena of quite a different kind, as we discuss here. The contribution of the bond-pair degrees of freedom to thermal properties is obtained here from the lattice free-energy functional using MC simulation, as mentioned in the preceding paragraph. The results for the superfluid density or superfluid stiffness ps, a quantity measured e.g. via the penetration depth, are discussed. As shown, its doping and temperature dependence compare well with experimental results. In this chapter, I also report the calculation of the fluctuation specific heat Cv(T) and find that there are two peaks in its temperature dependence, a sharp one connected with Tc (ordering of the phase of m)and a relatively broad one(hump)connected to T* (rapid growth of the magnitude of Δm). The former is specially sensitive to the presence of a magnetic field, as we find in agreement with experiment. Vortices are relevant excitations in a superconductor and, in particular, in 2D orquasi-2D systems vortices influence the finite temperature properties in a major way. The results for the temperature dependence of vortex density obtained in the MC simulation of the GL-like model are also mentioned in Chapter 4. I report an estimate of the correlation length as well. These results might have relevance for the large Nernst signal observed over a broad temperature range above c in cuprates, as pointed out there. Properties of an isolated vortex and collective effects arising due to interaction between vortices are of much significance for understanding mixed state of type-II superconductors and thus of cuprates. The superconducting order is destroyed in the core region around the centre of a vortex and the vortex core carries signatures of the normal state in a temperature regime where it is generally unattainable due to occurrence of superconductivity. As mentioned in Chapter 5, vortex properties(e.g. electronic excitation spectrum at the vortex core) in BCS superconductors have been explored theoretically, at a microscopic level through the Bogoliubov-deGennes(BdG) theory as well as using the Ginzburg-Landau functional. However, properties of vortices in cuprate superconductors have been found to be much more unusual than could possibly be captured by straightforward extensions of BCS theory to a -wave symmetry case. Chapter 5 briefly reviews the experimental findings on vortices in the superconducting state of cuprates, mainly as probed by Scanning Tunnelling Microscopy(STM) as well as from other probes such as NMR, neutron scattering, SR etc. I discuss some of the consequences of our GL-like functional regarding vortex properties, namely that of the vortex core and the region around it. We use our model to find Δm and m at different sites m for a 2π vortex whose core is at the midpoint of a square plaquette of Cu lattice sites. The vortex is found to change character from being primarily a phase or Josephson vortex for small x to a more BCS-like or Abrikosov vortex with a large diminution in the magnitude Δm as one approaches the vortex core, for large . Here I do not make any direct comparison with experimental data but discuss implications of our results in the background of existing experimental facts. Unravelling the mysteries of high-Tc cuprates should necessarily involve the understanding of electronic excitations over a broad regime of doping and temperature encompassing the pseudo gap, superconducting and strange metal states. A phenomenological theory which aims to describe the pseudo gap phase as one consisting of preformed bond-pairs, is required to include both unpaired electrons and Cooper pairs of the same electrons coexisting and necessarily coupled with each other. In our Ginzburg Landau approach only the latter are explicit, while the former are integrated out. However, effects connected with the pair degrees of freedom are often investigated via their coupling to electrons, one very prominent examples being Angle Resolved Photoemmision Spectroscopy(ARPES),in which the momentum and energy spectrum of electrons ejected from the metal impinged by photons is investigated. In Chapter 6, we develop a unified theory of electronic excitations in the superconducting and pseudo gap phases using a model of electrons quantum mechanically coupled to spatially and temporally fluctuating Cooper pairs(the nearest neighbour singlet bond pairs). We discuss the theory and a number of its predictions which seem to be in good agreement with high resolution ARPES measurements, which have uncovered a number of unusual spectral properties of electrons near the Fermi energy with definite in-plane momenta. We show here that the spectral function of electrons with momentum ranging over the putative Fermi surface(recovered at high temperatures above the pseudogap temperature scale) is strongly affected by their coupling to Cooper pairs. On approaching Tc i.e. the temperature at which the Cooper pair phase stiffness becomes nonzero, the inevitable coupling of electrons with long-wavelength(d-wave symmetry) phase fluctuations leads to the observed characteristic low-energy behavior as reported in Chapter 6. Collective d-wave symmetry superconducting correlations develop among the pairs with a characteristic correlation length ξ which diverges on approaching the continuous transition temperature Tc from above. These correlations have a generic form for distances much larger than the lattice spacing. As we show here, the effect of these correlations on the electrons leads, for example, to a pseudogap in electronic density of states for T > T c persisting till T* , temperature-dependent Fermi arcs i.e. regions on the Fermi surface where the quasiparticle spectral density is non zero for a zero energy excitation and to the filling of the antinodal pseudogap in the manner observed. Further, the observed long-range order(LRO) below c leads to a sharp antinodal spectral feature related to the non zero superfluid density, and thermal pair fluctuations cause a deviation(‘bending’) of the inferred ‘gap’ as a function of k from the expected d-wave form (cos kxa - cos kya). The bending, being of thermal origin, decreases with decreasing temperature, in agreement with recent ARPES measurements. I conclude in Chapter 7 by mentioning some natural directions in which the functional and the approach used here could be taken forward. The phenomenological theory proposed and developed in this thesis reconciles and ties together a range of cuprate superconductivity phenomena qualitatively and confronts them quantitatively with experiment. The results, and their agreement with a large body of experimental findings, strongly support the mechanism based on nearest neighbor Cooper pairs, and emergence of long-range -wave symmetry order as a collective effect arising from short range interaction between these pairs. This probably points to the way in which high-c superconductivity will be understood.

Water provision in rural areas represents a significant challenge, especially within the context of resource and sanitation in developing countries. High set-up costs, lack of installation expertise and reliability issues, arising from fluctuating operational conditions, have prevented many people from receiving the full benefit of automated pumping systems. The specific aim of this thesis is to assess the feasibility of using a tunable, induced flow subsystem as a means of optimising the power utilization and performance of a centrifugal pump over a wider range of operating conditions than typically expected. More generally, the research presented is undertaken to reduce the high implementation costs and localised limitations of rural water pumps by developing the theory towards a ‘’one-size-fits-all’’ pumping system. The theoretical analysis of an induced flow centrifugal pumping system is presented, coupled with the analogous electrical system. The results of simulations performed using both systems are compared to experimental results, obtained using an induced flow subsystem (IFS) test rig constructed at the University of Liverpool. All sets of results demonstrate consistent IFS characteristics, identifying its capability to maintain maximum power point (MPP) operation of the centrifugal pump irrespective of load. Further, the experimental results reveal a boost in output pressure which enables the pump to achieve an improved hydraulic power and increased operating range over the same system without an IFS. It is concluded that, through the addition of an IFS, the performance of a centrifugal pump may be decoupled from its operating head, expanding its range of serviceable conditions and demonstrating potential to develop a ‘’one-size-fits-all’’ system. Ultimately, this could offer a cheaper and more reliable supply of a resource which is vital to life in any rural location: clean water.