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A plethora of physical, chemical, biological and even social processes, can be modelled by mathematical equations. Many of these processes involve continuous change, and then the relevant equations take the form of differential equations. In models containing more than one variable, which is the great majority of situations, the relevant equations are called partial differential equations (PDEs). Given that these equations are instrumental in modelling the world around us, it is crucial that appropriate tools are developed for solving PDEs so that the associated models can be properly analysed. PDEs come into two broad categories: linear and non-linear. A general technique for solving linear PDEs was developed by the great French mathematician Fourier in the early 1800s. Non-linear PDEs are much more difficult to solve analytically. In 1997 the PI introduced a new method for solving a large class of non-linear PDEs. In an unexpected development, these results have motivated the development of a completely new method for solving linear PDEs in two dimensions. This is remarkable, since until then it was thought that the methods developed by Fourier and others in the 18th century could not be improved. This method is reviewed by three authors in the March 2014 issue of the Journal SIAM Review in the article titled "The Method of Fokas for solving linear PDEs", and in an accompanied editorial the importance of this method for solving linear PDEs is compared with the importance of the "Fosbury flop" in the high jump. The first part of this project involves completing the implementation of the above method to some important linear and non-linear problems in two dimensions, and then extending this method from 2 to 3 dimensions. Several medical imaging techniques, including Computed Tomography, Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) are based on the solution of a particular class of mathematical problems, called inverse problems. In the second part of this project, new numerical and analytical techniques will be implemented for PET and SPECT. The Riemann function occurs in many different areas of mathematics. Several conjectures related to the Riemann function remain open, including the famous Riemann hypothesis and the Lindeloef hypothesis. The third part of the project involves the analysis of the asymptotics of the Riemann and related functions, which is expected to enhance our understanding of the relevant, most important mathematical structures.

Young's famous double-slit experiment of 1803 demonstrated that light behaves as a wave. The light emerging from the slits has a characteristic intensity pattern originating from constructive and destructive interference. Later it was found that when single particles (photons or even molecules) pass through a double slit they produce similar interference patterns; this experiment became the key piece of evidence for wave-particle duality. A Mach-Zender interferometer is similar to Young's double-slit setup, except that light is split into two routes using mirrors. When the light is recombined, constructive or destructive interference occurs, depending on the difference in the phase of the light from the two routes. Subtle differences in the path-length, or refractive index, can easily be detected, because they determine the phase difference, and thus they control the interference. This project aims to synthesise and test a "molecular Mach-Zender interferometer" consisting of a molecule with two charge-transport paths; interference between the two transmission channels controls whether the whole system is conductive (in phase) or non-conductive (out of phase). Thus these molecules are expected to be sensitive to magnetic or electric fields which can change the relative phases of the two channels. Furthermore quantum interference effects tend to produce sharp changes in transmission with electron energy, which can result in strong thermoelectric effects. This project is concerned with exploring fundamental principles, but in the long term, this research has the potential to generate commercially disruptive technologies, such as thermoelectric devices for scavenging thermal energy, and transistors with reduced power requirements, abrupt switching and small footprints. This project if a thoroughly integrated collaboration of three research groups focusing on (1) Oxford: design and synthesis of molecular structures, (2) Liverpool: testing of single molecule conductance and thermopower, and (3) Lancaster: theory and computational simulation, to guide the interpretation of the experimental data, and the design of new molecular structures. At present there exists a no-man's land between the 15-nm length scale accessible to top-down technologies, such as electron-beam lithography, and bottom-up technologies such as chemical synthesis. The molecules investigated in this project are 3 nm across, but can be increased in size up to around 10 nm. This project is therefore a significant step towards bridging this crucial technology-scale gap, at the limit of Moore's law.

The UK Government has an ambitious target of reducing CO2 emissions by 80% by 2050, and energy demand reduction will have to play a major part in meeting this goal. While traditional research on mitigation of carbon emissions has focused on direct consumption of energy (how we supply energy, what types of fuel we use, and how we use them etc.), the role that materials and products might play in energy demand reduction is far less well studied. One third of the world's energy is used in industry to make products, such as buildings, infrastructure, vehicles and household goods. Most of this energy is expended in producing the key stock materials with which we create modern lifestyles - steel, cement, aluminium, paper, and polymers - and we are already very efficient in producing them. A step change in reducing the energy expended by UK industry can therefore only come about if we are able to identify new ways of designing, using, and delivering products, materials and services. Before firm recommendations can be made to decision-makers regarding the combined technical and social feasibility of new products and material strategies, a fundamental set of research questions will need to be addressed. These concern how various publics will respond to innovative proposals for product design, governance and use. For example, more energy efficient products may need to operate differently or look very different, while a significant shift from an ownership model to a service delivery model (e.g., direct car ownership to car clubs and rental) can also deliver considerable material efficiency and energy demand reduction. Will members of the wider public and key decision-makers welcome, oppose, or actively drive such supply chain innovations, and what are the implications of knowledge about public views for decision-makers in the corporate and government sector? Understanding the answers to these questions is the main focus of this project. The research led by Cardiff University, and partnered with the Green Alliance, will combine qualitative and quantitative social science methodologies - in particular expert interviews and workshops, deliberative research and a (GB) national survey. The project has 4 phases, spanning a 45 month period. Work Package 1 involves initial work with UK INDEMAND partners, and interviews with industry and policy representatives, to identify the assumptions being made about people and society in key pathways for materials energy demand reduction. Work Package 2 involves four workshops - held in Edinburgh, Cardiff, London and a rural location - where members of the public will deliberate the identified pathways to change. In Work Package 3 we will conduct a nationally representative survey of 1,000 members of the British public, further exploring public perspectives on ways of designing and changing our use of materials. A particularly innovative aspect of the project is a set of targeted policy engagement activities (in Work Package 4) where we will hold workshops, interviews and other direct stakeholder involvement, exploring the implications of the findings about public views with key decision-makers in UK businesses, policy and the political sphere (including Parliamentarians through the Green Alliance's Climate Leadership programme for MPs). Along with the empirical data gathered in Work Packages 1, 2, and 3, the activities in Work Package 4 will allow us to formulate clear recommendations for action on achieving a reduction in UK final energy consumption through bringing knowledge of social barriers and opportunities to bear on governmental policy and industry decision-making about innovative materials and products delivery/use.

The development of technologies that exploit quantum physics to improve measurement, information processing, and communication is an area of rapid growth. Quantum devices such as memories and processors operate at different optical frequencies, typically outside the telecom range where losses in fibre are minimal. The goal of this studentship is to develop frequency-conversion techniques using nonlinear optics in optical fibre that will allow individual photons to be shifted between different wavelength bands. This will enable communication between the nodes of quantum devices operating at different optical frequencies; it will also allow low-loss, (and hence long-distance) exchange over fibre as well as photon conversion to frequencies where optimal detectors operate. To be of value, use of quantum frequency translation must allow any small or large photon frequency shift within the visible and near infrared. The frequency conversion must also not alter properties of the photon other than its wavelength, including any entanglement with other systems. Furthermore, it should be highly efficient while not introducing additional 'noise' photons. To meet the above requirements, frequency conversion of single photons will be investigated in photonic crystal fibre (PCF), optical fibres with a matrix of air holes running along their length, as well as subclasses of PCF such as bandgap fibre and hybrids thereof. In order to achieve this, new fibres will need to be designed and then fabricated in the university's state-of-the-art fibre fabrication facility. The project will involve theoretical and numerical analysis, fabrication, laboratory work using cutting-edge equipment, and participation in project meetings and reporting. Hence the full range of skills required for high-impact scientific research will be developed as well as communication and transferrable skills. There will be opportunities to present work at leading international conferences and to publish in high-quality peer-reviewed journals. The project will be carried out in close collaboration with other members of the Networked Quantum Information Technologies hub being led by the University of Oxford, providing the opportunity to work on this individual experiment and simultaneously contribute to a larger joint research effort.

The proposed research will provide the first proof-of-principle for a new family of Compressed Quantitative Magnetic Resonance Imaging (CQ-MRI), able to rapidly acquire a multitude of physical parameter maps for the imaged tissue from a single scan. MRI is the pre-eminent imaging modality in clinical medicine and neuroscience, providing valuable anatomical and diagnostic information. However, the vast majority of MR imaging is essentially qualitative in nature providing a `picture' of the tissue while not directly measuring its physical parameters. In contrast, quantitative MRI aims to measure properties that are intrinsic to the tissue type and independent of the scanner and scanning protocol. Unfortunately, due to excessively long scan times, Quantitative MRI is not usually included in standard protocols. The proposed research is based on a combination of a new acquisition philosophy for Quantitative MRI, called Magnetic Resonance Fingerprinting, and recent advances in model-based compressed sensing theory to enable rapid simultaneous acquisition of the multiple parameter maps. The ultimate goal of the research will be to produce a full CQ-MRI scan capability with a scan time not substantially longer than is currently needed for a standard MRI scan.

The aim of this project is design two implants systems that can communicate with each other through a wireless scheme.

The project will develop a mobile lifelogging platform that will deliver measures of cardiovascular disease in an everyday situation, such as driving a car. Driving represents a common daily activity, where experiences and expressions of anger have implications for health and safety. As such, this activity can be associated with high levels of negative emotions that have a cumulative impact on long-term health. Lifelogging is the continuous act of recording and documenting our lives, from the things we do, to the places we visit and even our feelings. Wearable cameras and body sensors allow us to capture rich information from multiple data sources about ourselves. As sensors become more prevalent, within our environment, the range of available data is increasing. This has enabled lifelogs to become richer with information and their use in various application domains, such as digital health, is increasing. The project will explore how multiple streams of physiological and contextual data can be processed and integrated in real-time to detect the user's state. Measures such as heart rate, pulse wave velocity (PWV), speed of the vehicle, location, and first-person photographs of the environment will be brought together to identify instances of anger and inflammation. A range of signal processing approaches will be applied to these data items (e.g. inter-beat interval from the heart rate will be subjected to Fast Fourier Transform) and artefacts will be identified and either removed or incorporated in real-time. Currently, it is straightforward to log overt aspects of behaviour, such as photographs, location and movement. However, this project will combine those markers with covert changes in cardiovascular physiology, which aren't perceived directly by the user. Hence, the project is extending a person's awareness of their bodies, how their behaviour and reactions to situations are directly impacting their bodies and the triggers for such behaviour, e.g. traffic congestion at a junction may raise our heart rate, without the user being consciously aware of this physiological change. Repeating this stressful behaviour daily, over a sustained period, could contribute to the development of cardiovascular disease. Reviewing moments when arterial inflammation occurs and understanding the context of this behaviour leads to an enhanced perception of how daily events affect health. This can lead to positive changes to the person's lifestyle, such as avoiding the junction in question to help prevent triggers leading to the onset of cardiovascular disease. The system will provide a new method to monitor and influence behaviour, which enables us to enhance and bring the field of lifelogging into alignment with advances in digital health. This is achieved using markers that are clinically relevant in the context of lifelogging technologies and developing techniques to process multi-modal signals in real-time. To the best of the author's knowledge, the integration of such biomedical markers that measures physiological changes in context to prevent the onset of disease has not been addressed in any other developments. Overall, the project attempts to reduce a significant real-world problem with an advanced mobile lifelogging platform. The platform will be evaluated in a real-world scenario to assess its capabilities outside of an artificial environment. This will enable us to gauge its robustness as a real and practical solution to log and quantify behaviour. In this way, the data collected will be used to identify moments of arterial inflammation and the context of those times to promote self-reflection and the implementation of behavioural changes.

Our concept of a distributed electrical and environmental sensor system to enable unprecedented flexibility and reduction of cost in deploying innovative measurement, control and protection functions for the power network requires to be proven in the context of relevant industry standards, with particular emphasis on current and voltage measurements. Consequently, the core research idea of this proposal is to assess the feasibility of this undertaking through systematic research and implementation of a range of innovative error compensation methods. In particular, the feasibility study will aim to demonstrate that metering and protection accuracy classes for voltage and current transducers are attainable by this technology. In order to address the objectives of the project, the research programme will be subdivided into specific work packages. The scope and methodologies adopted with respect to the individual tasks are described in the Case for Support attachment under the following work packages: WP1. Engagement with stakeholders (Month 1-12) WP2. Design and simulation of transducers and experiments. (Month 1-7) WP3. Assembly and packaging of electrical current and voltage transducers. (Month 4-7) WP4. Characterisation and environmental/high-voltage stress testing of transducers (Month 7-12) WP5. Development and testing of sensor interrogation hardware and software. (Month 1-12)

Recent large-scale laboratory tests of the curved Mark 1 CCell paddle and its control system, conducted with TSB funding #131499, have demonstrated the predicted four-fold increase in performance to cost ratio compared to other wave energy devices. Preliminary sea trials of components are ongoing and the technology is now ready for mid-stage development to build a complete system. This project takes lessons learned from Mark 1 system development and incorporates them into a Mark 2 Wave Energy Converter (WEC) technology package based on the CCell paddle, its control and its foundation system. The project aims to demonstrate cost-effective performance of an array of CCell paddles. This will be achieved through optimisation of the shape of the curved paddle and Power Take Off (PTO) for a wide range of sea conditions. Intelligent proactive control algorithms will be developed to maximise power capture in the highly variable conditions that operating devices will experience. Numerical tools developed and validated as part of the preceeding project will be extended to study interactions between arrays of CCell paddles. Co-operative PTO control strategies will be developed to optimise array performance, matching demanded power with generated power and balancing against device loading and degradation. Prototype systems will be constructed and tested both in laboratory conditions and at sea to validate concepts. Successful completion of the project will bring CCell and associated technology to the pre-commercial stage. Economic viability will be established and the barriers preventing the uptake of competitor technology will be removed.

Two of the most critical global challenges currently being faced are energy security and climate change. In the UK, more than £100 bn of investment in new UK power stations and grid infrastructure is projected within the next decade, both to replace ageing plant and to allow for the incorporation of renewable sources. Such changes will involve a paradigm shift in the ways in which we generate and transmit electricity. Since a central element of all items of power plant is electrical insulation, meeting our future challenges through the deployment of new innovative plant, this will require the development and exploitation of new high performance insulation material systems. Polymer nanocomposites have demonstrated clear potential, but the lack of detailed understanding of the underlying physics and chemistry is a major impediment to the technological realisation of this potential. In certain laboratory studies, nanodielectrics materials have out-performed unfilled and traditional micro-composite insulating materials. However, entirely contrary results have also been elsewhere. Undoubtedly, this variability in macroscopic behaviour comes about as a consequence of our inability to define and control the key factors that dictate the dielectric behaviour of nanocomposites. The overarching aim of this project is to resolve this issue such that the potential of dielectric nanocomposites - nanodielectrics - can be fully exploited. As such, the project is totally aligned with the EPSRC Materials for Energy theme in which it is accepted that "in the field of advanced materials it will be necessary to strengthen approaches to the rational design and characterisation of advanced materials and their integration into structures and systems". It also aligns with the Advanced Materials theme of the "Eight Great Technologies", it which it is accepted that "these materials are essential to 21st century manufacturing in a UK market worth £170 billion per annum and representing 15 per cent of GDP". Our research hypothesis is that the macroscopic properties of nanodielectrics cannot be reliably controlled without understanding the processes that occur at the interfaces between the matrix material and the nanoparticles, because these regions directly affect two critical issues. First, interfacial interactions will affect the nanoparticle dispersion, which has a major bearing on many physical properties and, second, the nature of the interface determines the local density of states in the system, and thereby the material's overall electrical characteristics. To understand such local processes is challenging and we propose to do this through a combination of computation simulation and experiment, where both aspects are closely aligned, thereby allowing the simulation to direct experiment and the experimental result to refine the simulation. The work programme has been divided in 3 distinct themes, which will progressively move the work from fundamentals to exploitation. Theme 1 will therefore concentrate on model systems, where simulation and experiment can be most closely aligned. Theme 2 will then seek to deploy the key messages to the development of technologically relevant systems and processes. Throughout, Theme 3 will engage with a range of stakeholders that will range from key industry players (equipment manufacturer s, energy utilities, standards bodies) to the general public t maximise the reach and significance of its ultimate impact (economic, environmental, societal). We see the involvement of our Industrial Users Group as being particularly important, both in helping to guide the project and in terms of ensuring acceptance of the technologies that will ultimately arise.