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Priscian is an emblematic figure of the Graeco-Roman world of late antiquity; my study focuses on the ability of grammar to account for socio-cultural factors. In the first chapter, the reading of the preface to Priscian's Ars places him within an established cultural framework in which Greek sources are seen as a foundation of knowledge for any kind of Latin study. The linguistic approach taken by Priscian to describe Latin grammar reflects the beliefs and the expectations of his readership, and the status of standard language as perceived by the contemporary elites. Priscian's work is evidence of the importance placed by the elites on knowledge of both Greek and Latin as a means to gain prestige and respectability in the competitive society of late antiquity. In the second and third chapters, a metalinguistic analysis of the last two books of the Ars, the De constructione, provides an insight into Priscian's method of transferring Greek elements into Latin, and helps us to shape his audience. Priscian did not merely accomplish a grammatical work; in describing and codifying the grammar of a language he synthesised a vision of a world. The fourth and fifth chapters offer a close analysis of the linguistic data used by Priscian to describe Latin syntax, namely literary quotations, and exempla ficta. They reflect a codified standard written language which had become by the sixth century a mark of distinction for elites, despite the spoken language taking different developments. Elites in Constantinople considered this language deeply shaped by Greek grammar, a fact that provides guidance for the interpretation that elites had of their identity. The pairing of Latin with Greek syntax enables Priscian and his readers to bridge differences on issues concerning identity and provides us with a key for understanding the idea of the Graeco-Roman world of sixth century.

The purpose of this thesis is to interrogate the stylist forms and literary devices employed in the travel writing of Cyprus with particular attention to how they relate to the political history of the island from the time of British imperial rule, to the rise of nationalist movements, and the ethnolinguistic partition of 1974. Doing so, this thesis uses the concept of transportal literatures to interrogate how these works manoeuvre through these political paradigms in the writings of Cyprus. From its earliest representations in English, the island has been depicted as a limen between cultural spaces, including Asia and Europe and East and West. It is through this literary motif that travel writers frame Cyprus as a portal through which they can explore their own ethnic, national, or gendered identities. The setting exists as a gateway between different ideas of culture and, consequently, as a gateway through which mobile travel writers understand their post/colonial identifications - including British and Cypriot writers alike. It is important to trace the intertextual links between these authors whose works explicitly respond to one another. These texts are chosen to complicate our understanding of the postcolonial discipline: Cyprus, home to two British military bases, and under partial Turkish 'occupation', sits in an ambivalent juncture between colonisation and independence. Writers reacting to this - lingering British imperialism, the double hegemonies of Greece and Turkey, the partition dividing islanders - reveal a need to transport notions of nations, cultures, and identities beyond expected binary lines.

This thesis focuses on well-posedness and stability estimates (i.e. continuous dependence with respect to the nonlinearities) for a family of cross-diffusion systems that includes several models used to describe cell diffusion in Mathematical Biology for one or more species. We discuss rigorous quantitative results for a class of (possibly degenerate) parabolic PDEs, including scalar equations as well as systems. The approach is typical of Analysis of PDEs, hence the concepts of weak solutions in Sobolev spaces, a priori estimates and well-posedness are crucial. Considering scalar, nonlinear diffusion, we extend the existing solvability, uniqueness, boundedness and stability results. Regarding non-degenerate models for multiple species, we work in the framework of systems with an entropy structure and a limited set of other assumptions that allow us to prove stability estimates, improving some of the existing results. Finally, we have been working on the multi-species, degenerate case, providing a continuous dependence estimate under suitable (but rather restrictive) assumptions. Two different types of numerical simulations are presented in order to complement the abstract results.

This dissertation focuses on the problem of order in the political thought of Aristotle and the Confucian philosopher Mencius. It attempts to reconstruct this ancient and perennial problématique by investigating its etymological, cosmological, metaphysical, psychological, ethical, and political implications. It argues that order was conceived in both authors as the combination of normative and aesthetic aspects, and that rational as well non-rational elements need to be taken into account in order to provide a comprehensive understanding of the question. Unlike modern renditions of the problem, which put emphasis on either of the two aspects, it is argued that Aristotle and Mencius were similarly concerned about accounting for a more inclusive interpretation of order, one which overcomes well-known dichotomies such as transcendence/immanence, unity/multiplicity, body/mind. Moreover, while equating order with goodness and beauty, they were also aware of the limits of order in practical contexts. The problem of order, on the one hand, has its unifying theme in the abstraction of a universal moral norm; on the other hand, because order always necessarily implies some degree of disorder, it also possesses an inherently contextual and practical dimension. In this last respect, both Aristotle and Mencius held complex and sophisticated views on the moral psychology, which represents the link between a metaphysical conception of order and its socio-political instantiation. The problem of order, it is argued, provides a very fruitful case for comparing the ancient Greek and Chinese traditions of thought, and for rethinking the very concept of order in political theory and international relations. In particular, order represent a notion which avoids, more than other concepts, the risk of essentialism, reification, or of imposition of alien schemes of thought upon different cultural traditions.

Xylella fastidiosa is a xylem-limited, Gram-negative, gammaproteobacterium, and the causal agent of Pierce’s disease (PD) of grapevine and several other diseases in many economically important crops. In the PD patho-system in California, it is natively vectored by the blue green sharpshooter (Graphocephala atropunctata) and vectored by the invasive glassy-winged sharpshooter (Homalodisca vitripennis). When transmitted into a healthy vine, X. fastidiosa colonizes the xylem leading to blockages both directly through biofilm formation and EPS build up and indirectly through the induction of tyloses and pectin gels. These blockages are believed to contribute to symptom development which includes marginal leaf necrosis, abscission of the leaf blade from the petiole, green islands in the periderm, desiccation of the berries, and eventually vine death. While there is no current cure, common management practices include severe pruning of diseased tissue and insecticide sprays to control vector populations. However, new management strategies are needed to create cost effective and sustainable solutions to protect these culturally valuable crops.As of late, biological control agents, the enhancement of existing treatments, and the development of transgenic disease-resistant or disease-tolerant plants have been implemented in an attempt to cope with phytopathogenic microbes. First, the concept of a biological control agent or biocontrol can be defined as the use of a third organism to act antagonistically against a pathogen and lessening disease symptoms in the host. This antagonism can occur via antibiotic production, direct predation, or nutrient competition and exclusion. We have identified two endophytic bacterial isolates that impart varying levels of protection to the grapevine from X. fastidiosa and have speculated on the mechanisms by which they do so. Second, the transgenesis of plants has been proven to be effective at controlling pathogens. Transcriptomic data can be used to identify genes that are upregulated in a successful defense response against a pathogen and these genes can be transgenically engineered to be overexpressed and confer resistance or tolerance. Here, we have overexpressed a class III peroxidase and found that it conferred tolerance to the grapevines against X. fastidiosa. Third, metal ions have recently been found to break down the resistance of some pathogenic bacteria to certain antibiotics. We investigated the in vitro activities of copper, a common metal used in vineyards, on X. fastidiosa. We found that it affects several characteristics such as cell surface hydrophobicity and cell attachment to a surface. We found that it also increases the susceptibility of X. fastidiosa cells in a biofilms to antibiotics. Collectively, this research has set the framework for the development of novel PD management strategies and can potentially serve as a model for other X. fastidiosa patho-systems affecting other economically important crops.

This thesis motivates and examines the use of methods from topological data analysis in detecting and analysing topological features relevant to models from statistical physics and particle physics. In statistical physics, we use persistent homology as an observable of three different variants of the two-dimensional XY model in order to identify relevant topological features and study their relation to the phase transitions undergone by each model. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and demonstrate its use in detecting topological defects called vortices. By considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length. In particle physics, we investigate the use of persistent homology as a means to detect and quantitatively describe center vortices in SU(2) lattice gauge theory in a gauge-invariant manner. The sensitivity of our method to vortices in the deconfined phase is confirmed by using twisted boundary conditions which inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a k-nearest neighbours classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical β and critical exponent of correlation length for the deconfinement phase transition. We also use persistent homology to study the stability of vortices under gradient flow and the classification of different vortex surface geometries.

Within the past decade, machine learning algorithms have been proposed as a potential solution to a variety of research problems which emerge within physics. As this cross-fertilization matures, one is able to investigate if the efficiency of machine learning algorithms can be increased by interpreting them physically and if there exist fundamental connections that can be established between the two research fields. In this thesis, we pursue research directions intimately related to the above questions. First, we investigate the practical implications of interpreting machine learning functions as statistical-mechanical observables. Through this perspective, we explore if we can extend the classification capabilities of machine learning algorithms and if we are able to include neural networks within Hamiltonians to induce phase transitions in systems. A related direction concerns the use of machine learning to construct inverse renormalization group transformations to arbitrarily increase the size of a system. These techniques are then utilized to study the infinite volume limit of discrete spin systems and of quantum field theories, in order to investigate if machine learning is a powerful tool to study phase transitions. In another research direction we explore the derivation of machine learning algorithms from quantum field theories. We investigate if the φ4 scalar field theory satisfies the Hammersley-Clifford theorem and if it can be recast as a Markov random field. We then explore if φ4 neural networks can be derived that generalize a certain class of standard neural network architectures, and we present relevant numerical applications. Finally, we discuss how this research direction opens up the opportunity to investigate machine learning within quantum field theory and how it solidifies a rigorous connection between the research fields of machine learning, probability theory, statistical mechanics, lattice and constructive quantum field theory.

Lightning is an extremely energetic electric discharge process in our atmosphere. Lightning activity is used as an indicator for the nowcasting of severe weather, significantly affects atmospheric chemistry, and threatens electrical and electronic devices. Yet, our fundamental understanding of atmospheric electricity is far from complete. For example, new processes above thunderclouds have been discovered which are collectively known as Transient Luminous Events (TLEs) and Terrestrial Gamma ray Flashes (TGFs). This PhD project aims to characterize and improve on a thunderstorm detector recently developed by private industry to warn of local lightning activity at airports. Most existing lightning location systems rely on sub-ionospheric propagating radio waves. The new technique measures the displacement currents induced on an electrode exposed to changes in the atmosphere's electric field between 1-45 Hz, associated with all forms of lightning and wind-blown space charge. The unique dataset provided by this instrument has been investigated to (1) design a noise rejection and waveform recognition algorithm based on machine learning methods; (2) identify the source of anomalously strong current transients detected in fair-weather and their link to TLEs; (3) provide the first multi-instrumental analysis of thunderstorms producing superbolts and TLEs in the UK and northern Europe; (4) study the contribution of global lightning activity and associated Schumann Resonances (SR) on the quasi-electrostatic currents measured at Portishead (UK) during a 5-year period. This work indicates that the technique can be profitably used to prevent the risk posed to humans and infrastructures by intense lightning discharges, and additionally suggests a broad range of new applications for this method in atmospheric electricity research.

Yang-Mills theories based on the symplectic groups - denoted by Sp(2N) - are interesting for both theoretical and phenomenological reasons. Sp(2N) theories with two fundamental Dirac fermions give rise to pseudo-Nambu-Goldstone bosons which can be interpreted as a composite Higgs particle. This framework can describe the existing Higgs boson without the need for unnatural fine-tuning. This justifies a programme of wider investigations of Sp(2N) gauge theories aimed at understanding their general behaviour. In this work, we study the glueball mass spectrum for Sp(2N) Yang-Mills theories using the variational method applied to Monte-Carlo generated gauge configurations. This is carried out both for finite N and in the limit N → ∞. The results are compared to existing results for SU(N) Yang-Mills theories, again, for finite- and large-N. Our glueball analysis is then used to investigate some conjectures related to the behaviour of the spectrum in Yang-Mills theories based on a generic non-Abeliangauge group G. We also find numerical evidence that Sp(2N) groups confine both for finite and large N. As well as studying the glueball spectrum, we examine the quenched-meson spectrum for fermions in the fundamental, antisymmetric and symmetric representations for N = 2 and N = 3. This study enables us to provide a first account of how the related observables vary with N. The investigations presented in this work contribute to our understanding of the non-perturbative dynamics of Sp(2N) gauge theories in connection with Higgs compositeness and, more in general, with fundamental open problems in non-Abelian gauge theories such as confinement and global symmetry breaking.

In this Ph.D. Thesis we consider two specific supergravities which are well-established within the literature on holography, and which are known to provide the low-energy effective description of either superstring theory or M-theory: the six-dimensional half-maximal theory of Romans, and the maximal supergravity in seven dimensions. We implement their dimensional reduction by compactifying on an S1 and T2, respectively, to obtain a five-dimensional sigma-model coupled to gravity. Spectra of bosonic excitations are computed numerically by considering field fluctuations on background geometries which holographically realise confinement. We furthermore propose a diagnostic tool to detect mixing effects between scalar resonances and the pseudo-NambuGoldstone boson associated with spontaneous breaking of conformal invariance: the dilaton. This test consists of neglecting a certain component of the spin-0 fluctuation variables, effectively disregarding their back-reaction on the underlying geometry; where discrepancies arise compared to the complete calculation we infer dilaton mixing. For both theories this analysis evinces a parametrically light dilaton. For each supergravity we uncover a tachyonic instability within their parameter space; motivated by these pathological findings we proceed to conduct an investigation into their respective phase structures, reasoning that there must necessarily exist some mechanism by which these instabilities are rendered physically inaccessible. We compile a comprehensive catalogue of geometrically distinct backgrounds admissible within each theory, and derive general expressions for their holographically renormalised free energy F. Another numerical routine is employed to systematically extract data for some special deformation parameters, and F is plotted in units of an appropriate universal scale. Our analysis proves fruitful: each theory exhibits clear evidence of a first-order phase transition which induces the spontaneous decompactification of the shrinking circular dimension before the instability manifests, favouring instead a class of singular solutions. The aforementioned dilaton resonance appears only along a metastable portion of the branch of confining backgrounds.

Drifting ionospheric irregularities in the form of inhomogeneities in the electron density distribution can affect the propagation of Global Navigation Satellite System (GNSS) signals causing fluctuations in amplitude and phase. Such fluctuations in amplitude and phase of the signals with shorter periods arise from small-scale irregularities and are known as scintillation. Typically, scintillation is accompanied by temporal fluctuations in Total Electron Content (TEC): that is, fluctuations in the phase of the signals with longer periods arising from large-scale irregularities. Large-scale irregularities tend to cascade into small-scale irregularities owing to instability mechanisms. Whilst this is the case for the equatorial ionosphere, at high-latitudes, such energy cascade does not seem to be as developed. Consequently, mainly phase scintillation tends to be detected on GNSS at auroral and polar latitudes. TEC fluctuations can be used as a proxy to indicate the presence of phase fluctuations induced by large-scale irregularities at high-latitudes. Scintillation and TEC fluctuations can significantly impact the performance of GNSS particularly in equatorial latitudes and high-latitudes ionosphere. Scintillation can be modelled by means of propagation through phase-changing screens which are thin irregular layers across a propagation path used to approximate a stochastic medium between a transmitter and a receiver. The thesis aims to characterise the spatial distribution of electron density irregularities along profiles in the E and F layer transverse to GPS ray paths and their impact on GPS signals at high-latitudes. To achieve this, in 2018 and 2019, multi-instrument experimental campaigns were designed and conducted involving the European Incoherent SCATter (EISCAT)/EISCAT Svalbard Radar (ESR) UHF radars and geodetic GNSS receiver stations of relevance at the auroral and polar latitudes. It is worthy to clearly mention here that the data collected from these experiments were utilised in the research. EISCAT UHF/ESR radar beams were used to infer the distribution of electron density irregularities along hypothetical phase screens in which EISCAT UHF/ESR electron density profiles were measured along hypothetical phase screens alternately intersecting GNSS ray paths at different ionospheric shell heights. In this investigation, representative case studies were considered in the auroral and polar ionospheres. Whilst auroral irregularities seemed to be originated mainly by particle precipitation, polar irregularities could arise from polar patches and/or particle precipitation. The effects of electron density irregularities distributed along phase screens across GNSS ray paths of relevance were investigated in terms of temporal fluctuations in TEC and positioning performance. These experiments provide information about the outer scale of the phase screens and the likely spatial distance over which auroral and polar irregularities distribute. The electron density distribution along a given phase screen, that is whether it is symmetrical or not, and the origin of the phase screens were also considered. The results provide insight into the impact of adverse space weather conditions on real-time and post-processing positioning applications at auroral and polar latitudes.

The impact the ionospheric electron density has on satellite-based applications, such as satellite communication and navigation systems, is of important consideration, as these signals must propagate through the ionosphere. The excess signal delay due to the ionospheric electron density is one of the main error sources in Global Navigation Satellite Systems (GNSS). One method to study the global behaviour of electron density is ionospheric tomography, a technique that allows estimation of the electron density in the ionosphere through line-integral observations between GNSS satellites and receivers. The research presented in this thesis benefits from the Multi Instrument Data Analysis System (MIDAS) (Mitchell and Spencer, 2003), an ionospheric tomography software that was originally capable of producing global or regional three-dimensional ionospheric electron density reconstructions from GPS observations. GPS-based ionospheric tomography is first assessed in this thesis. This method shows accurate results in regions with high density of ground receivers. However, regions with sparse or uneven ground-receiver coverage give rise to geometric limitations, which lead to large errors in electron density estimation. To overcome this, a multi-GNSS (GPS-GLONASS-Galileo) based ionospheric imaging method is presented in this thesis. The method combines observations from different constellations of satellites orbiting around the Earth, which improves the availability and coverage of measurements for a given receiver network. The technique is evaluated for both under quiet and disturbed geomagnetic conditions, through simulation as well as experiment. The analysis quantifies the improvement of multi-GNSS tomography over single-GNSS tomography for electron density imaging in the ionosphere. The electron density images can be used to apply corrections to ionospheric delay in precise positioning algorithms. Many GNSS precise positioning algorithms rely on ionospheric corrections to calculate the position. However, there is still room for improvement in reducing atmospheric and ionospheric induced errors. Application of corrections from multi-GNSS tomography is therefore proposed in this thesis to support GNSS positioning. Ionospheric corrections from a global network of multi-GNSS receivers are used in a single-frequency positioning method. The results show that this approach allows positioning accuracies comparable to dual-frequency positioning to be obtained, confirming the potential of using ionospheric corrections from multi-GNSS tomography.

Travelling ionospheric disturbances, or TIDs, are wavelike features propagating in the ionosphere. TIDs are studied for many reasons, such as their effects on GNSS navigation and their connection to natural disasters like earthquakes and tsunamis. Sensitive instruments and reliable techniques are required to accurately image and detect the ionospheric perturbations. The primary purpose of this thesis is to evaluate and advance the capabilities of tomographic methods to image TIDs for scientific purposes, which also has a potential application to GNSS positioning in the presence of TIDs. This thesis therefore also quantifies the potential impact of TIDs on state-of-the-art ionospheric correction services, for e.g. Network Real-Time Kinematic (N-RTK) positioning, that occur when the corrections are interpolated for an approximate rover position. Building on these results, a novel TID-mitigation strategy is also tested. Simulations with different methods of interpolation for N-RTK ionospheric corrections show that TIDs can induce errors large enough to merit attention. For positioning in the presence of TIDs, a weighted least-squares interpolation technique is modified to adapt to estimated TID directions and wavelengths. The new methods are shown, in simulation tests and a case study, to decrease the number of large interpolation errors that may impede fast integer ambiguity resolution. Electron density maps generated by ionospheric tomography can also provide an alternative approach to TID mitigation. The MIDAS (Multi-Instrument Data Analysis System) tomography algorithm is therefore tested to determine its suitability for TID imaging. As an initial test, a case study is presented a where MIDAS is used to image a large-scale TID over North America occurring during a geomagnetic storm. The resulting images are verified with in-orbit measurements and ionosonde soundings. Further tests are conducted with simulated data generated with varying TIDs characteristics and satellite geometries, including geostationary orbits. The results show that most TIDs are reconstructed well by MIDAS, with the smaller MSTIDs a possible exception. Electron density images generated from these results can be used for TID mitigation in positioning, and also aid studies into TID and gravity wave generation mechanisms. Together, the results from studies emphasise the importance of satellite and receiver geometry in TID observation and mitigation. The simulation-based tomography results show the benefits of including geostationary satellite geometry in ionospheric tomography, while results from the LSTID case study and interpolation simulations illustrate the importance of a well distributed ground receiver network.

Electrical impedance tomography (EIT) is an imaging technique for mapping the internal conductivity distribution of an object by taking voltage measurements from electrodes attached to the surface of the object, while an electrical current is injected to these boundary electrodes. EIT has been researched in many different application areas in the world as a simpler, cheaper and safer alternative to many other tomography techniques, while provider very useful and often unique functional information. The main aim of this PhD study is to extend the use of EIT by further improvements of our understanding of the EIT data and image analysis and its challenges. In each case the challenges are highlighted and some solutions are proposed. EIT has great applications in area of industrial processes. We highlight a challenges associated with the EIT to simultaneously reconstruct the permittivity and conductivity, in particular, when there is a low contrast in permittivity values of samples but in high contrast with background. A good case study to highlight this challenge is a water dominate oil and gas flow with important application in process industry. The thesis is proposing a dual-modality EIT with transmission mode travel time ultrasound tomography for such an application. Another potential area with the EIT is the use of EIT for artificial skin for robotics application. This is done using a soft material such as fabric and the skin can be developed by EIT with sensing the change in conductivity while pressure applied to the skin. We have identified two main issues with the application, one the need to extend the functionality of the skin to be dynamical. This will enable the EIT based skin to work as an interface allowing social interaction with the robot. Second is a well established issue in medical EIT, which also exists in robotics EIT and that is the movement of electrodes which corrupted the EIT image. We have developed a spatially correlated total variation imaging algorithm so that the robot skin using EIT could work as dynamical imaging sensor allowing for interactive skin. The interaction of the EIT based skin through pressure sensing can be done like a movie rather than individual images, which resembles the human skin interaction. The movement of electrodes and electromechnaicl interpretation of pressure via EIT image are both very difficult problems to model and interpreter. For these issue we implemented a convolutional neural network deep learning algorithm. The imaging results shows very good performance of both spatially correlated TV algorithm together with the deep learning approach. The working flow of this dissertation can be explained as the following sections. Firstly, the basic background of EIT, its applications and mathematical theories including the forward problem, inverse problem have been reviewed. Secondly, a complex impedance image reconstruction is developed. The complex EIT which is determining conductivity and permittivity distribution at the same time using the real and imaginary part of the voltage measurements are presented. A complexvalued forward model, Jacobian matrix, inverse solution and related simulation studies are developed as well, the results indicated there are still challenging in reconstructing both parameters simultaneously. And then, a novel EIT combined with ultrasound transmission mode tomography (UTT) dual-modality for threephase material image is developed. Identification of three phase oil/gas/water in water dominated situation should be possible via complex EIT, but practicality this is challenging. Therefore, the EIT/UTT dual modality imaging can be deployed for such application, where EIT is used to identify non-conductive phase which either oil or gas phase and hence UTT is used to identify air phase. Both simulation and experimental studies are implemented and a image fusion method is proposed for producing three-phase images. Finally, a conductive fabric based EIT dynamical sensing system integrated with deep learning for improving image quality is proposed, a movie like denoised experimental results are presented using a spatiotemporal total variation algorithm and a convolutional neural network training. The deep learning method helps overcoming the imaging artefact's due to electrode movement which is a main issue in fabric based EIT.

Correlation distances in the ionosphere are important for ionospheric data assimilation models that must balance modelled parameters against real observations. Many communication systems that transmit radio signals in the HF band rely on such models in order to operate accurately. However, defining the correlation distance is difficult because of the considerable variations present in the ionospheric regions and the lack of dense observations to measure them. In such cases, models have to entrust that an observation can be extrapolated away from its source, which if wrong can introduce errors in the ionospheric representation. In this research, the correlation distance in the ionosphere is examined from the perspective of two instruments: the ionosonde and the HF ground-to-ground sounder. Both provide observations of the bottomside ionosphere through time delay and in the latter case also by angle of arrival. Initially the research focussed on the analysis of HF angle- of- arrival (AoA) observations to characterise and understand the effects of travelling ionospheric disturbances (TIDs) from a dedicated campaign, part of the USA High-Frequency Geolocation and Characterisation Program (HFGeo). It was found that nowcasting the TIDs was critically important for the application of HF geolocation. Having established this, the foundation questions for the rest of the research were to find the ground density of instrumentation required for ionospheric modelling – hence finding the correlation distances. The analysis turned to Europe where a network of suitable ionosondes existed with a long-term dataset that would allow an evaluation over multiple years. The initial analysis of the similarity between the ionosonde data from different stations observed inconsistencies between using Pearson’s correlation coefficient and root-mean-square error (RMSE). A new approach was implemented, called Taylor diagrams, that is capable of summarising multiple statistical parameters onto a single graph in order to produce a similarity measure. The research further studied the diurnal cycle phase offset in the foF2 measurements from the European ionosondes and phase synchronisation method was developed that that increased the East-West correlation distance twofold. The research then allowed the new correlation method to be used on the HFGeo data from the USA during calm and TID affected ionospheres. It was shown that the correlation distance was dependent not only on the severity of the ionospheric conditions but also on the height of the reflection layer and the sampling frequency of the ionosonde. The chapter showed that during TIDs the ionosonde correlation distance can be reduced below 147±17 km and during very strong disturbances – to 47±15 km. However, in a manner analogous to the diurnal cycle in the foF2 measurements, the results indicated that most of the decorrelation was due to the mismatch of the phase front of the passing TIDs across the region. In response to the need to track and model the phase front of TIDs, a technique called Feature Based Dynamic Time Warping (FDTW) was applied to vertically and horizontally synchronise the phase offset between ionosonde density profiles. This technique was demonstrated to operate successfully in tracking TIDs across the region of interest. The research has implications for the density of observations needed of the bottomside ionosphere for mapping the ionosphere to provide support applications such as HF communications and geolocation. This in turn is important for the deployment of instrumentation and the correlation distances applied in algorithms for data assimilation.

The main purpose of this thesis is to develop a better understanding of the interfaces between materials in spatial and time domains via 2D and 3D visualisation and quantitative parameter measurement using Electrical Resistance Tomography (ERT). Some advantages of ERT have been reported as being high temporal resolution, low-cost and non-radiation emitting. The ERT modality is generally used to visualise the interior of a region by mapping the conductivity distribution using potential difference that is measured by electrodes that are attached to the medium. The main algorithm for image reconstruction that has been used is total variation regularisation due to its potential for producing high-quality images with sharp boundaries. In this work, a series of simulation studies and lab-based phantom experimental tests were conducted. Contributions of this thesis are generally categorised into three aspects. First of all, a spatial-temporal total variation based on the Split Bregman method has been proposed for analysing dynamical movement of a target in a circular tank based on 2D ERT, where spatial and temporal gradients were employed for exploring performance in the space and time domains, and time response of dynamical ERT images has been proposed for the comparison and illustration of advantages of sharp dynamical images. Furthermore, the proposed STTV has extended to 3D ERT visualisation, where a tank with the shape of a vertical pipe has been designed with a dual-plane aiming at representing interior information by producing dynamical images of a moving target inside the pipe. Velocity measurements are feasible based on 2D/3D ERT and the cross correlation method, and the accuracy of these were discussed. Moreover, planar array for 3D ERT visualisation was used to overcome the issue that 3D ERT visualisations based on traditional electrode-ring sensors would suffer from low resolution on the axis-direction along the pipe, especially the region between rings where electrode-ring gaps lead to missing data. Results showed that ERT planar array can extract additional information in its detectable region with a higher 3D spatial resolution, and a combination of planar array and ring-electrode ERT can potentially be made for the purpose of exploring more information in a pipeline. In general, this thesis represents the research works on improving the performance of static/dynamical ERT visualisation and quantitative parameter measurements. These works have potential applications in flow imaging and tomography-based measurement or control systems in the future. Detailed applications and further work are suggested. Although ERT is a new imaging technique and lots of issues are still preserved to be solved, it is believed that such research would have contributions to the future development of electrical impedance tomography research.

Radio signals propagating through the ionised upper atmosphere (the ionosphere) in low latitude regions of the world can experience amplitude scintillation. This could threaten safety-critical applications of satellite navigation such as aviation. The research presented here studied the effects of amplitude scintillation on a Septentrio PolaRxS geodetic receiver and a Garmin 480 aviation receiver by means of a Spirent GNSS constellation simulator. Different types of fade profiles showed that an abrupt drop in signal strength caused a loss of lock on the signal more often than a profile with a slow, gradual fade. A performance comparison of the two receivers demonstrated that the aviation receiver was more vulnerable than the geodetic receiver. An unexpected loss of lock at a specific fade duration and depth was seen with the Garmin receiver and was not explained. A single fade with a long fade duration was more likely to cause a loss of signal lock compared to rapid multiple fades. Scintillation on signals from low elevation satellites can significantly degrade the precision and integrity of the navigation solution in an aviation receiver; especially if the satellites are within the best geometrical set. RAIM was observed to be no longer available during the critical landing approach phase of the scenario, in the case when all satellites in view were affected by the scintillation-induced signal perturbations. A technique was also developed to simulate L5 scintillation based on real scintillation events of L1, in the absence of real captured data for L5. This was done to enable future investigations on aviation receiver performance when both L1 and L5 frequencies experience scintillation. Analysis indicated that L5 signal can be more vulnerable to the scintillation compared to the L1 signal, which may have important implications for aviation safety.

The great majority of algorithms employed in the study of lattice field theory are based on Monte Carlo's importance sampling method, i.e. on probability interpretation of the Boltzmann weight. Unfortunately in many theories of interest one cannot associated a real and positive weight to every configuration, that is because their action is explicitly complex or because the weight is multiplied by some non positive term. In this cases one says that the theory on the lattice is affected by the sign problem. An outstanding example of sign problem preventing a quantum field theory to be studied, is QCD at finite chemical potential. Whenever the sign problem is present, standard Monte Carlo methods are problematic to apply and, in general, new approaches are needed to explore the phase diagram of the complex theory. Here we will review three of the main candidate methods to deal with the sign problem, namely complex Langevin dynamics, Lefschetz thimbles and density of states method. We will first study complex Langevin dynamics, combined with the gauge cooling method, on the one-dimensional Polyakov line model, and then we will apply it to pure gauge Yang-Mills theory with a topological theta-term. It follows a comparison between complex Langevin dynamics and the Lefschetz thimbles method on three toy models, which are the quartic model, the U(1) one-link model with a mu dependent determinant, and the SU(2) non abelian one-link model with complex beta parameter. Lastly, we introduce the density of state method, based on the LLR algorithm, and we will employ it in the study of the relativistic Bose gas at finite chemical potential.

In this thesis we investigate numerically SU(2) theories with Dirac—or Majorana—fermions in the adjoint representation. Majorana fermions have historically proven difficult to treat numerically; here, a change of basis is introduced that allows two Majorana fermions to be expressed in terms of one Dirac fermion. This also provides greater insight into the analysis of the properties of theories with Dirac fermions. Attention is focused on the SU(2) theory with a single Dirac flavour (or equivalently two Majorana flavours). Its lattice phase diagram, spectrum, and the anomalous dimension of the chiral condensate are investigated. We observe a long region of constant mass ratios and an anomalous dimension 0.9 ≲ γ∗ ≲ 0.95. The behaviour of the pion mass and the presence of a light scalar in particular point to behaviour that is not traditionally confining; instead the theory appears to lie in or near the conformal window. The topological susceptibility and instanton size distribution are also investigated, for the one-Dirac-flavour theory and additionally the pure-gauge and two-Dirac-flavour (Minimal Walking Technicolor) theories. The properties are found to not depend on number of flavours, indicating a quenching of the fermions in the topology, also consistent with (near-)conformal behaviour (as has previously been reported in studies of other observables for Minimal Walking Technicolor). The code used is described, and a high-performance computing benchmark developed from it is detailed. While the benchmark was originally developed to investigate the performance of different supercomputer architectures for the class of problems we are interested in. Due to the nature of the code on which it is based, it has an unusual flexibility in the demands it may place on machine’s performance characteristics, which may allow it to be applicable to problems outside of lattice physics. The benchmark is used to characterise a number of machines’ relative performance.