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The wastewater treatment process (WWTP) plays a critical role in providing clean water. However, emerging and predominately unregulated, bioactive chemicals such as steroids and pharmaceutical drugs are being increasingly detected in surface waters that receive wastewater effluent. Although present at low concentrations, their inherent bioactive nature has been linked to abnormalities in aquatic organisms and there are also water reuse and human health implications. As part of the urban water cycle, the WWTP is the gatekeeper to the surface waters e.g. rivers. Pharmaceuticals enter wastewater treatment from inappropriate disposal of unused drugs to the sink/toilet or via landfill. Prescribed or illicit drug use also has the inevitable consequence of being metabolised in the human body (to parent, Phase I / II metabolites) and excreted in urine, which subsequently enters the WWTP. Coupled with naturally produced and excreted bioactive steroids, the challenge for wastewater treatment is that it was never designed to remove these bioactive chemicals and is inefficient. Evaluating the prevalence and fate of a steroid or pharmaceutical in the WWTP is challenging as human enzymatic metabolism causes the bioactive chemical to exist in multiple forms - parent, Phase I and Phase II metabolites. Phase II metabolites predominate urine excretion and are the starting products entering the wastewater environment. They therefore act as the precursors to the biotransformations that take place during treatment and produce the Phase I and/or parent forms of the bioactive chemical. Before treatment technologies can be developed and evaluated for pharmaceutical and steroid removal in the WWTP, our understanding needs to improve on how the different bioactive chemical forms behave, and their relationships to each other. This means identifying the biotransformations between metabolites and parent forms. To achieve this requires a move from targeted analysis - we analyse for what we expect to see - to develop methods that are non-targeted and search for Phase II metabolites and their associated Phase I / parent forms. Drawing on inspiration from metabolomics approaches used in the biosciences, the aim of this proposal is to develop a novel non-target method to identify bioactive chemical Phase II metabolites and their biotransformation products in wastewater. Knowledge of Phase II metabolite occurrence and fate in the wastewater environment is important in assessing the impact of user behaviour, process and environmental factors or bioactive chemical parent removal. This will inform on WWTP efficiency, provide data for optimising models that predict pharmaceuticals and steroids, and evaluate environmental risk.

A primary goal of organic chemists is the construction of molecules for applications as diverse as medicines, new materials and biomolecules. The field is constantly driven by the need for new, more efficient methods as well as ways to access molecules which may have previously been impossible. The most important tool at an organic chemist's disposal is undoubtedly catalysis, whereby the use of a small amount of a custom-designed catalyst can permit a reaction to occur under much milder conditions than otherwise, or opens up new chemical pathways altogether. For this reason, innovation in catalysis is central to innovation in organic chemistry. Nature's catalysis is performed by enzymes; evolution has made them phenomenally efficient. Often playing a leading role in enzymatic processes are 'hydrogen bonds', special types of electrostatic attraction which are important in facilitating the chemical reaction between two molecules by bringing them into close proximity with one another or by stabilising the pathway leading to product formation. My research seeks to employ these same interactions, but in the context of small molecules which we can readily synthesise and handle in the lab. This approach to catalysis is very exciting as it is still in its infancy yet offers exciting opportunities for both activation and control. This project will seek to take inspiration from a distinct field within chemistry called Supramolecular Chemistry, which explores the behavior of large molecules which are assembled from smaller ones using multiple weak 'temporary' interactions working in tandem. Hydrogen bonds are very important in this regard but there are a number of other key interactions such as ion pairs and pi-cation interactions which have been shown to be powerful in building up molecular structures. It is our aim to apply several of these interactions together in tandem to design new catalysts that will bind with our reactant in a very well defined orientation. The catalyst will also induce the substrate to react with another molecule, allowing the selective synthesis of one mirror image of a molecule over the other (so-called enantiomers). This is a very important pursuit in science, since the inherent 'handedness' of biological systems means that the different mirror image forms of chiral molecules often have very different effects in the body. This is of particular importance in pharmaceutical applications.

The product rule of the all familiar operation of taking derivatives of real valued functions has a plethora of generalisations and applications in algebra. It leads to the notion of derivations of algebras - these are linear endomorphisms of an algebra satifying the product rule. They represent the classes of the first Hochschild cohomology of an algebra. The first Hochschild cohomology of an algebra turns out to be a Lie algebra, and more precisely, a restricted Lie algebra if the underlying base ring is a field of positive characteristic. The (restricted) Lie algebra structure extends to all positive degrees in Hochschild cohomology - this goes back to pioneering work of Gerstenhaber on defornations of algebras. Modular representation theory of finite groups seeks to understand the connections between the structure of finite groups and the associated group algebras. Many of the conjectures that drive this area are - to date mysterious - numerical coincidences relating invariants of finite group algebras to invariants of the underlying groups. The sophisticated cohomological technology hinted at in the previous paragraph is expected to yield some insight regarding these coincidences, and the present proposal puts the focus on some precise and unexplored invariance properties of certain groups of integrable derivations under Morita, derived, or stable equivalences between indecomposable algebra factors of finite group algebras, their character theory, their automorphism groups, and the local structure of finite groups.

Spectrum is a precious but scarce natural resource. In the UK, Ofcom will free up the analogue TV spectrum at 800MHz (together with the available 2.6GHz band) for 4G, which has already raised £2.34 billion for the national purse. According to Ofcom, the amount of data Britons consume on the move each month has already hit 20 million gigabytes, mainly due to users' engagement of video, TV and films while on the move. It is also a common understanding for the mobile operators that by 2020 a 1000 times increase in the system capacity will be needed to avoid mobile networks grinding to a halt. Maximising spectral efficiency, which is limited by interference and fading for wireless networks including 4G, is therefore a major issue. An emerging idea, which is championed by Alcatel-Lucent and has already received serious consideration by vendors and operators is that of a massive MIMO antenna system. This technology has the potential to unlock the issue of spectrum scarcity and to enhance spectrum usage tremendously by enabling simultaneous access of tens or hundreds of terminals in the same time-frequency resource. In order for massive MIMO technology to attain its utmost potential, it is important that various challenges in terms of channel estimation and acquisition due to pilot contamination, fast spatial-temporal variations in signal power and autonomous resource allocation, in particular in the presence of simultaneous access of a large number of users need to be addressed. The focus of this project is on tackling these fundamental challenges, by advancing aspects of information theory, estimation theory and network optimisations. In particular, we will contribute in terms of modelling massive MIMO channels underpinned by heterogeneous correlation structures; performing information theoretic analysis in terms of random matrix theory through shrinkage estimators; robust precoder design for massive MIMO in the presence of channel estimation errors; developing novel channel estimation technique in the presence of severe pilot contamination; and proposing and analysing game theoretic algorithms for autonomous resource allocation and pilot assignments. All the concepts and algorithms developed will be integrated and the radio link layer performance will be assessed using a simulation reference system based on LTE-Advanced standards and its evolution towards 5G. Industrial partners will be engaged throughout the project to ensure industrial relevance of our work.

While the theory of minimal and constant mean curvature (CMC) surfaces is a purely mathematical one, such surfaces overtly present themselves in nature and are studied in many material sciences. This makes the theory more exciting. If we take a closed wire and dip it in and out of soapy water, the soap film that forms across the loop is in fact a minimal surface and the physical properties of soap films were already studied by Plateau in the 1850s. The air pressure on the sides of soap films is equal and constant. However, if we change the pressure on one side, for instance by blowing air on it, the new surface that we obtain is what we call a soap bubble. A soap bubble is a CMC surface. More precisely, minimal and CMC surfaces are, respectively, mathematical idealisation of soap films and soap bubbles. The mean curvature of a soap film and bubble is a quantity that is proportional to the pressure difference on the sides of the film. The value of the pressure difference, and therefore of the mean curvature, is zero for a soap film/minimal surface and it is non-zero constant for a soap bubble/CMC surface. Since the pressure inside a small bubble is greater than the pressure inside a big one, the constant mean curvature of a small bubble is greater than the constant mean curvature of a big one. Minimal and CMC surfaces also enjoy crucial minimising properties relative to area. Among all surfaces spanning a given boundary, a soap film/minimal surface is one with locally least area; soap bubbles/CMC surfaces locally minimise area under a volume constraint. This project aims to investigate several key geometric properties of minimal and CMC surfaces. Roughly speaking, I intend to prove several results about CMC surfaces embedded in a flat three-dimensional manifold, including area estimates when the surfaces are compact with bounded genus and the ambient manifold is compact. I also plan to study the limits of a sequence of minimal or CMC surfaces embedded in a general three-dimensional manifold.

This project aims to develop, and to provide a range of mechanisms to support interdisciplinary collaborations that use and develop new mathematics for understanding climate variability and impact on resilience. Focusing on three scientific themes the project will nurture connections between mathematicians, statisticians, environmental scientists, policy makers and end users working in impact areas to help to identify high-risk and high-return research that will develop collaborations in the areas of the themes. We will do this by a range of tools, including a series of managed events (workshops, sandpits, study groups and e-seminars) that will focus on specific problems to end users as well as promoting novel collaborations in the areas of scientific focus. We will provide a mechanism to solicit, evaluate and fund proposals for feasibility studies that work across this area. This will be informed by an expert panel of researchers as well as an advisory panel taken from national and international groups and end-users.

The goal of this Korea-UK research initiative is to address Research theme 1 (Innovative concepts from Electrodes to stack) of the EPSRC-KETEP Call for Collaborative Research with Korea on Fuel Cell Technologies. The proposal also covers some aspects of Research theme 2 (Predictive control for performance and degradation mitigation). Hence, this research is associated with improving the lifetime and performance of polymer electrolyte fuel cells. Within this project we will develop new corrosion resistant catalyst supports and catalyse those supports utilising a new catalysis technique. We will also examine the development of porous bipolar plates and see how we can integrate those bipolar plates and catalysts within a fuel cell. We will trial the materials in test stacks and look at the performance and longevity of these new materials. Parallel to this work, we will use state of the art x-ray tomography and other imaging techniques to assess the performance of the materials under real operating conditions. Information from these tests will allow us to develop a methodological framework to simulate the performance of the fuel cells. This framework will then be used to build more efficient control strategies for our higher performance fuel cell systems. We will also build a strong and long-lasting collaborative framework between Korea and the UK for both academic research and commercial trade. The project will benefit from the complementary strengths of the Korean and UK PEFC programmes, and represents a significant international activity in fuel cell research that includes a focus on the challenging issues of cost reduction and performance enhancement. The project will have particularly high impact and added value due to a strong personnel exchange programme with researchers spending several months in each other's labs; highly relevant industrial collaboration; and links with the H2FC Supergen. We have strong support from industrial companies in both the UK and Korea who will support our goals of developing new catalysts for fuel cells (Amalyst - UK, and RTX Corporation - Korea), new corrosion resistant porous bipolar plates (NPL-UK; Hyundai Hysco and Hankook tire (Korea)), and fuel cell and system integrators (Arcola Energy and Intelligent Energy (UK)).

Computational fluid dynamics (CFD) is fundamental to modern engineering design, from aircraft and cars to household appliances. It allows the behaviour of fluids to be computationally simulated and new designs to be evaluated. Finding the best design is nonetheless very challenging because of the vast number of designs that might be explored. Computational optimisation is a crucial technique for modern science, commerce and industry. It allows the parameters of a computational model to be automatically adjusted to maximise some benefit and can reveal truly innovative solutions. For example, the shape of an aircraft might be optimised to maximise the computed lift/drag ratio. A very successful suite of methods to tackle optimisation problems are known as evolutionary algorithms, so-called because they are inspired by the way evolutionary mechanisms in nature optimise the fitness of organisms. These algorithms work by iteratively proposing new solutions (shapes of the aircraft) for evaluation based upon recombinations and/or variations of previously evaluated solutions and, by retaining good solutions and discarding poorly performing solutions, a population of optimised solutions is evolved. An obstacle to the use of evolutionary algorithms on very complex problems with many parameters arises if each evaluation of a new solution takes a long time, possibly hours or days as is often the case with complex CFD simulations. The great number of solutions (typically several thousands) that must be evaluated in the course of an evolutionary optimisation renders the whole optimisation infeasible. This research aims to accelerate the optimisation process by substituting computationally simpler, dynamically generated "surrogate" models in place of full CFD evaluation. The challenge is to automatically learn appropriate surrogates from a relatively few well-chosen full evaluations. Our work aims to bridge the gap between the surrogate models that work well when there are only a few design parameters to be optimised, but which fail for large industry-sized problems. Our approach has several inter-related aspects. An attractive, but challenging, avenue is to speed up the computational model. The key here is that many of these models are iterative, repeating the same process over and over again until an accurate result is obtained. We will investigate exploiting partial information in the early iterations to predict the accurate result and also the use of rough early results in place of the accurate one for the evolutionary search. The other main thrust of this research is to use advanced machine learning methods to learn from the full evaluations how the design parameters relate to the objectives being evaluated. Here we will tackle the computational difficulties associated with many design parameters by investigating new machine learning methods to discover which of the many parameters are the relevant at any stage of the optimisation. Related to this is the development of "active learning" methods in which the surrogate model itself chooses which are the most informative solutions for full evaluation. A synergistic approach to integrate the use of partial information, advanced machine learning and active learning will be created to tackle large-scale optimisations. An important component of the work is our close collaboration with partners engaged in real-world CFD. We will work with the UK Aerospace Technology Institute and QinetiQ on complex aerodynamic optimisation, with Hydro International on cyclone separation and with Ricardo on diesel particle tracking. This diverse range of collaborations will ensure research is driven by realistic industrial problems and builds on existing industrial experience. The successful outcome of this work will be new surrogate-assisted evolutionary algorithms which are proven to speed up the optimisation of full-scale industrial CFD problems.

This proposal focuses on the impact performance of state-of-the-art composites in the form of fibre-reinforced plastics (FRPs) with through-thickness reinforcement introduced via Z-pinning. The application of composites in primary lightweight structures has been steadily growing during the last 20 years, increasing the requirement for new and advanced composites technologies. Recent examples include large civil aircraft, such as the Boeing 787 and the Airbus A350, high performance cars, such as the McLaren 650S, and civil infrastructure, such as the Mount Pleasant bridge on the M6 motorway. FRPs are made of thin layers (plies) of plastic material with embedded high stiffness and strength fibres. The plies are bonded together in a stack by applying heat and pressure in a process known as "curing". The resulting assembly is the FRP laminate. The main reasons for the increasing usage of FRPs in several engineering fields are the superior in-plane specific stiffness and strength with respect to traditional alloys and the long-term environmental durability due to the absence of corrosion. Another key advantage of FRPs is that they can be tailored to specific design loads via optimising the orientation of the reinforcing fibres across the laminate stack. FRPs are, however, prone to delamination, i.e. the progressive dis-bond of the plies through the thickness of the laminate. This is due to the fact that standard FRP laminates have no reinforcement in the through-thickness direction, so the out-of-plane mechanical properties are significantly lower than the in-plane ones. According to the US Air Force, delamination can be held responsible for 60% of structural failures in FRP components in service. Impacts are the main cause of delamination in FRP laminates with energies usually in the order of 20J, sufficient to produce multiple delaminations in FRP plates. A representative scenario for such energy level is that of a 2cm diameter stone impacting a laminate at a speed of 110 km/h. In aerospace impact scenarios can be much more severe. For example, the certification of turbofan engines requires the fan blades to be able to withstand an impact with a bird whose mass is in the order of a few kilograms at speed in excess of 300 km/h, with impact energies of thousands of Joules. Introducing through-thickness reinforcement in FRPs is a viable strategy for improving the through-thickness mechanical properties and inhibiting delamination. Z-pinning is a through-thickness reinforcement technique whereby short FRP rods are inserted in the laminate before curing. Z-pinning has been proven to be particularly effective in inhibiting delamination under quasi-static, fatigue loading and low velocity/low energy impact loading. Nonetheless, little is known regarding the performance of Z-pinned laminates withstanding high energy/high speed impacts, whose effects are governed by complex transient phenomena taking place within the bulk FRP laminates and multiple ply interfaces. Overall, these phenomena are commonly denoted as "high strain rate" effects. There is some evidence that Z-pinning is beneficial also for high-speed impacts, but this is not conclusive. The current lack of knowledge may be circumvented with overdesign and expensive large-scale structural testing, but this is not a sustainable solution in a medium to long-term scenario. This project aims to fill the knowledge gap outlined above, by combining novel experimental characterisation at high deformation rates with new modelling techniques that can be used for the design and certification of impact damage tolerant composite structures. The development of suitable modelling techniques is particularly important for industrial exploitation, since it will reduce the amount of testing required for certification of composite structures, with a significant reduction of costs and shorter lead times to mark

The world's population is increasing and ageing so incidences of degenerative diseases (e.g. osteoporosis and osteoarthritis), bone cancer, and trauma are also increasing. Bone is currently the second most transplanted tissue after blood and without enough natural graft material available for transplantation, focus has shifted towards recruiting the body's natural regenerative properties by using temporary scaffolds to stimulate and support the healing process. Regenerative materials currently used in the clinic include bioceramics and degradable polyesters. However, bioceramics have serious limitations, such as a highly brittle nature, that exclude their use in cyclically loaded bone repair applications. Despite having regulatory approval, conventional polyesters degrade via autocatalysis making their degradation occur suddenly. It is essential that bespoke materials are synthesised that combine the strength and bioactivity of bioceramics with the toughness of polymers whilst also maintaining stringent control over the degradation rates, so that the material degrades concurrently with new tissue growth. In order to achieve this, the field of structural biomaterials must shift from focussing on conventional bioceramics and polyesters and instead embrace the opportunities available from bottom-up design and synthesis. New hybrid materials, with nanoscale interactions and bonding between co-networks of carefully designed tough degradable polymers and silica, will create a step change in biomaterials research and lead the way towards better osteochondral regeneration. Crucial to this step change is the design of new polymers with well-defined molecular size, architectures, chemical composition and degradability. This requires a synergy between materials engineering, polymer chemistry and cell culture. Acrylate based polymers synthesised with techniques that will enable control of molecular weight and composition will be used. These polymers will contain important functional groups. Key aspects are controlling the hydrophilicity of the hybrid and type of bonding between the polymer and the silica. The degree of hydrophilicity dictates the degree of swelling and to obtain optimal cell attachment. While acrylates are not inherently degradable, chains that are small enough to pass through the kidneys can be linked by biodegradable crosslinks, hence the need for control of size of the acrylate chains. The type of bonding (covalent or dynamic or combinations of) will determine the mechanical properties and rate of degradation. The hybrid materials will be fabricated into 3D porous structures, by developing a novel 3-D printing approach, where the hybrid sol will be directly printed. Due to the complexity of the materials and the interdependence of processing variables, it is essential that the structure of materials are understood at multiple length scales. State of the art techniques will be employed to probe and optimise the materials' structures from the nano- to macro-scale with respect to cellular response. An essential component for clinical success is that all stakeholders (clinicians and medical device companies) play an early role in scaffold development and technology transfer. The success of this interdisciplinary and complementary team, spanning polymer and inorganic chemistry; materials processing; hierarchical characterisation; cell biology; orthopaedic surgery; and technology transfer, will encourage internationally renowned researchers to move to and stay in the UK. Within 20-50 years, the UK will experience significant impact, speeding up return to work and maintaining the population's activity into older age. This exciting and innovative project bringing together international and UK collaborators will focus on developing a dynamic and supportive research environment. This project will produce leaders of new fields created by this project and ensures that the UK remains at the forefront of Biomaterials research.