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The Circular Economy (CE) is a revolutionary alternative to a traditional linear, make-use-dispose economy. It is based on the central principle of maintaining continuous flows of resources at their highest value for the longest period and then recovering, cascading and regenerating products and materials at the end of each life cycle. Metals are ideal flows for a circular economy. With careful stewardship and good technology, metals mined from the Earth can be reused indefinitely. Technology metals (techmetals) are an essential, distinct, subset of specialist metals. Although they are used in much smaller quantities than industrial metals such as iron and aluminium, each techmetal has its own specific and special properties that give it essential functions in devices ranging from smart phones, batteries, wind turbines and solar cells to electric vehicles. Techmetals are thus essential enablers of a future circular, low carbon economy and demand for many is increasing rapidly. E.g., to meet the UK's 2050 ambition for offshore wind turbines will require 10 years' worth of global neodymium production. To replace all UK-based vehicles with electric vehicles would require 200% of cobalt and 75% of lithium currently produced globally each year. The UK is 100% reliant on imports of techmetals including from countries that represent geopolitical risks. Some techmetals are therefore called Critical Raw Materials (high economic importance and high risk of supply disruption). Only four of the 27 raw materials considered critical by the EU have an end-of-life recycling input rate higher than 10%. Our UKRI TechMet CE Centre brings together for the first time world-leading researchers to maximise opportunities around the provision of techmetals from primary and secondary sources, and lead materials stewardship, creating a National Techmetals Circular Economy Roadmap to accelerate us towards a circular economy. This will help the UK meet its Industrial Strategy Clean Growth agenda and its ambitious UK 2050 climate change targets with secure and environmentally-acceptable supplies of techmetals. There are many challenges to a future techmetal circular economy. With growing demand, new mining is needed and we must keep the environmental footprint of this primary production as low as possible. Materials stewardship of techmetals is difficult because their fate is often difficult to track. Most arrive in the UK 'hidden' in complex products from which they are difficult to recover. Collection is inefficient, consumers may not feel incentivised to recycle, and policy and legislative initiatives such as Extended Producer Responsibility focus on large volume metals rather than small quantity techmetals. There is a lack of end-to-end visibility and connection between different parts of techmetal value chains. The TechMet consortium brings together the Universities of Exeter, Birmingham, Leicester, Manchester and the British Geological Survey who are already working on how to improve the raw materials cycle, manufacture goods to be re-used and recycled, recycle complex goods such as batteries and use and re-use equipment for as long as possible before it needs recycling. One of our first tasks is to track the current flows of techmetals through the UK economy, which although fundamental, is poorly known. The Centre will conduct new interdisciplinary research on interventions to improve each stage in the cycle and join up the value chain - raw materials can be newly mined and recycled, and manufacturing technology can be linked directly to re-use and recycling. The environmental footprint of our techmetals will be evaluated. Business, regulatory and social experts will recommend how the UK can best put all these stages together to make a new techmetals circular economy and produce a strategy for its implementation.

The emerging era of exascale computing that will be ushered in by the forthcoming generation of supercomputers will provide both opportunities and challenges. The raw compute power of such high performance computing (HPC) hardware has the potential to revolutionize many areas of science and industry. However, novel computing algorithms and software must be developed to ensure the potential of novel HPC architectures is realized. Computational imaging, where the goal is to recover images of interest from raw data acquired by some observational instrument, is one of the most widely encountered class of problem in science and industry, with myriad applications across astronomy, medicine, planetary and climate science, computer graphics and virtual reality, geophysics, molecular biology, and beyond. The rise of exascale computing, coupled with recent advances in instrumentation, is leading to novel and often huge datasets that, in principle, could be imaged for the first time in an interpretable manner at high fidelity. However, to unlock interpretable, high-fidelity imaging of big-data novel methodological approaches, algorithms and software implementations are required -- we will develop precisely these components as part of the Learned EXascale Computational Imaging (LEXCI) project. Firstly, whereas traditional computational imaging algorithms are based on relatively simple hand-crafted prior models of images, in LEXCI we will learn appropriate image priors and physical instrument simulation models from data, leading to much more accurate representations. Our hybrid techniques will be guided by model-based approaches to ensure effectiveness, efficiency, generalizability and uncertainty quantification. Secondly, we will develop novel algorithmic structures that support highly parallelized and distributed implementations, for deployment across a wide range of modern HPC architectures. Thirdly, we will implement these algorithms in professional research software. The structure of our algorithms will not only allow computations to be distributed across multi-node architectures, but memory and storage requirements also. We will develop a tiered parallelization approach targeting both large-scale distributed-memory parallelization, for distributing work across processors and co-processors, and light-weight data parallelism through vectorization or light-weight threads, for distributing work on processors and co-processors. Our tiered parallelization approach will ensure the software can be used across the full range of modern HPC systems. Combined, these developments will provide a future computing paradigm to help usher in the era of exascale computational imaging. The resulting computational imaging framework will have widespread application and will be applied to a number of diverse problems as part of the project, including radio interferometric imaging, magnetic resonance imaging, seismic imaging, computer graphics, and beyond. The resulting software will be deployed on the latest HPC computing resources to evaluate their performance and to feed back to the community the computing lessons learned and techniques developed, so as to support the general advance of exascale computing.

The DART project aims to pioneer a ground-breaking capability to enhance the performance and energy efficiency of reconfigurable hardware accelerators for next-generation computing systems. This capability will be achieved by a novel foundation for a transformation engine based on heterogeneous graphs for design optimisation and diagnosis. While hardware designers are familiar with transformations by Boolean algebra, the proposed research promotes a design-by-transformation style by providing, for the first time, tools which facilitate experimentation with design transformations and their regulation by meta-programming. These tools will cover design space exploration based on machine learning, and end-to-end tool chains mapping designs captured in multiple source languages to heterogeneous reconfigurable devices targeting cloud computing, Internet-of-Things and supercomputing. The proposed approach will be evaluated through a variety of benchmarks involving hardware acceleration, and through codifying strategies for automating the search of neural architectures for hardware implementation with both high accuracy and high efficiency.

Machine learning offers great promise in helping us solve problems by automatically learning solutions from data, without us having to specify all details of the solution as in earlier computational approaches. However, we still need to tell machine learning systems what problems we want them to solve, and this is currently undertaken by specifying desired outcomes and designing objective functions and rewards. Formulating the rewards for a new problem is not easy for us as humans, and is particularly difficult when we only partially know the goal, as is the case at the beginning of scientific research. In this programme we develop ways for machine learning systems to help humans to steer them in the process of collecting more information by designing experiments, interpreting what the results mean, and deciding what to measure next, to finally reach a conclusion and a trustworthy solution to the problem. The machine learning techniques will be developed first for three practically important problems and then generalized to be broadly applicable. The first is diagnosis and treatment decision making in personalized medicine, the second steering of scientific experiments in synthetic biology and drug design, and the third design and use of digital twins in designing physical systems and processes. An AI centre of excellence will be established at the University of Manchester, in collaboration with the Turing Institute and a number of partners from the industry and healthcare sector, and with strong connections to the networks of best national and international AI researchers.

The last decade has seen staggering advances in our ability to acquire and process information at the single atom and single molecule levels. Both the scanning tunnelling microscope (STM) and its slightly younger sibling, the atomic force microscope (AFM), now enable individual atoms to be probed, positioned, and, in essence, programmed by exploiting control of an impressively wide variety of physicochemical processes and properties right down to the single chemical bond limit. In recent work by Andreas Heinrich's team at IBM Research Labs, the worlds of quantum information processing and not just nanotechnology, but atomtech, have excitingly been bridged. This opens up entirely new approaches to not just quantum computing* but much more energy-efficient classical information processing via spin control in solid state devices (whose power consumption is increasingly unsustainable for many applications.) Although exceptionally impressive, the single atom qubits achieved by the IBM team are fabricated and manipulated on a bespoke material system involving a thin oxide film on a metal substrate. This is unfortunately not the most technologically relevant or scalable of architectures. Our New Horizons application instead involves information processing, logic, and spin control at the single atom level in silicon, a material that remains at the very core of our information society and will likely remain there for quite some time to come. We will exploit recent advancements in the fabrication of atomic-scale Boolean gates by Bob Wolkow's team at the University of Alberta to develop a new spin logic architecture based on the surprising "innate" magnetism of electron orbitals created on an atomically sculpted silicon surface.

Development of materials has underpinned human and societal development for millennia, and such development has accelerated as time has passed. From the discovery of bronze through to wrought iron and then steel and polymers the visible world around has been shaped and built, relying on the intrinsic properties of these materials. In the 20th century a new materials revolution took place leading to the development of materials that are designed for their electronic (e.g. silicon), optical (e.g. glass fibres) or magnetic (e.g. recording media) properties. These materials changed the way we interact with the world and each other through the development of microelectronics (computers), the world wide web (optical fibre communications) and associated technologies. Now, two decades into the 21st century, we need to add more functionality into materials at ever smaller length-scales in order to develop ever more capable technologies with increased energy efficiency and at an acceptable manufacturing cost. In pursuing this ambition, we now find ourselves at the limit of current materials-processing technologies with an often complex interdependence of materials properties (e.g. thermal and electronic). As we approach length scales below 100s of nanometres, we have to harness quantum effects to address the need for devices with a step-change in performance and energy-efficiency, and ultimately for some cases the fundamental limitations of quantum mechanics. In this programme grant we will develop a new approach to delivering material functionalisation based on Nanoscale Advanced Materials Engineering (NAME). This approach will enable the modification of materials through the addition (doping) of single atoms through to many trillions with extreme accuracy (~20 nanometres, less than 1000th the thickness of a human hair). This will allow us to functionalise specifically a material in a highly localised location leaving the remaining material available for modification. For the first time this will offer a new approach to addressing the limitations faced by existing approaches in technology development at these small length scales. We will be able to change independently a material's electronic and thermal properties on the nanoscale, and use the precise doping to deliver enhanced optical functionality in engineered materials. Ambitiously, we aim to use NAME to control material properties which have to date proven difficult to exploit fully (e.g. quantum mechanical spin), and to control states of systems predicted but not yet directly experimentally observed or controlled (e.g. topological surface states). Ultimately, we may provide a viable route to the development of quantum bits (qubits) in materials which are a pre-requisite for the realisation of a quantum computer. Such a technology, albeit long term, is predicted to be the next great technological revolution NAME is a collaborative programme between internationally leading UK researchers from the Universities of Manchester, Leeds and Imperial College London, who together lead the Henry Royce Institute research theme identified as 'Atoms to Devices'. Together they have already established the required substantial infrastructure and state-of-the-art facilities through investment from Royce, the EPSRC and each University partner. The programme grant will provide the resource to assemble the wider team required to deliver the NAME vision, including UK academics, research fellows, and postdoctoral researchers, supported by PhD students funded by the Universities. The programme grant also has significant support from wider academia and industry based both within the UK and internationally.

A statement is quantified if it has a qualification such as "for all" or "there exists". Let us consider an example commonly encountered in high school mathematics when studying quadratics: "there exists x such that ax^2 + bx + c = 0 has two different solutions for x". The statement is mathematically precise but the implications are unclear: what restrictions does this statement of existence force upon us? Quantifier Elimination (QE) replaces such a statement by an equivalent unquantified one, in this case by "either a is not zero and b^2 - 4ac is greater than 0, or all of a=b=c=0". The quantifier "there exists" and the variable x have been eliminated. The key points are: (a) the result may be derived automatically by a computer from the original statement using QE; (b) QE uncovers the special case when a=0 which humans often miss! Solutions to QE problems are not numbers but algebraic descriptions which offer insight. In the example above QE did not provide solutions to a particular equation - it told us in general how the number of solutions depends on (a,b,c). QE makes explicit the mathematical structure that was hidden: it is a way to "simplify" or even "solve" mathematical problems. For statements in polynomials over real numbers there will always exist an equivalent formula without the quantification. However, actually obtaining the answer can be very costly in terms of computation, and those costs rise with the size of the problem. We call this the "doubly exponential wall" in reference to how fast they rise. Doubly exponential means rising in line with the power of a power, e.g. a problem of size n costs roughly 2^(2^n). When applying QE in practice, results may be found easily for small problems, but as sizes increase you inevitably hit the wall where a computation will never finish. The doubly exponential wall cannot be broken completely: this rise in costs is inevitable. However, the aim of this project is to "push back the wall" so that lots more practical problems may be tackled by QE. The scale here means that pushing the wall even a small way offers enormous potential: e.g. 2^(2^4) is less than 66,000 while 2^(2^5) is over 4 billion! We will achieve this through the development of new algorithms, inspired by an existing process (cylindrical algebraic decomposition) but with substantial innovations. The first innovation is a new computation path inspired by another area of computer science (satisfiability checking) which has pushed back the wall of another famously hard problem (Boolean satisfiability). The team are founding members of a new community for knowledge exchange here. The second innovation is the development of a new mathematical formalisms of the underlying algebraic theory so that it can exploit structure in the logic. The team has prior experience of such developments and is joined by a project partner who is the world expert on the topic (McCallum). The third innovation is the relaxation of conditions on the underlying algebraic object that have been in place for 40+ years. The team are the authors of one such relaxation (cylindrical algebraic coverings) together with project partner Abraham. QE has numerous applications, perhaps most crucially in the verification of critical software. Also in artificial intelligence: an AI recently passed the U. Tokyo Mathematics entry exam using QE technology. This project will focus on two emerging application domains: (1) Biology, where QE can be used to determine the medically important values of parameters in a system; (2) Economics where QE can be used to validate findings, identify flaws and explore possibilities. In both cases, although QE has been shown by the authors to be applicable in theory, currently procedures run out of computer time/memory when applied to many problem instances. We are joined by project partners from these disciplines: SYMBIONT from systems biology and economist Mulligan.

Ultra-short and ultra-intense laser pulses provide an impressive camera into the world of electron motion. Attoseconds and sub-femtoseconds are the natural time scale of multi-electron dynamics during the ionization and break-up of atoms and molecules. The overall aim of the proposed work is to investigate attosecond phenomena, pathways of correlated electron dynamics and effects due to the magnetic field of light in three and four-electron ionization in atoms and molecules triggered by intense near-infrared and mid-infrared laser pulses. Correlated electron dynamics is of fundamental interest to attosecond technology. For instance, an electron extracted from an atom or molecule carries information for probing the spatio-temporal properties of an ionic system with angstrom resolution and attosecond precision paving the way for holography with photoelectrons. Moreover, studies of effects due to the magnetic field of light in correlated multi-electron processes are crucial for understanding a variety of chemical and biological processes, such as the response of driven chiral molecules. Chiral molecules are not superimposable to their mirror image and are of particular interest, since they are abundant in nature. The proposed research will explore highly challenging ultra-fast phenomena involving three and four-electron dynamics and effects due to the magnetic field of light in driven atoms and during the break-up of driven two and three-center molecules. We will investigate the physical mechanisms that underly these phenomena and devise schemes to probe and control them. Exploring these ultra-fast phenomena constitutes a scientific frontier due to the fast advances in attosecond technology. These fundamental processes are largely unexplored since most theoretical studies are developed in a framework that does not account for the magnetic field of light. Moreover, correlated three and four-electron escape is currently beyond the reach of quantum mechanical techniques. Hence, new theoretical tools are urgently needed to address the challenges facing attoscience. In response to this quest, we will develop novel, efficient and cutting-edge semi-classical methods that are much faster than quantum-mechanical ones, allow for significant insights into the physical mechanisms, compliment experimental results and predict novel ultra-fast phenomena. These semi-classical techniques are appropriate for ionization processes through long-range Coulomb forces. Using these techniques, we will address some of the most fundamental problems facing attoscience. Our objectives are: 1) Identify and time-resolve novel pathways of correlated three-electron dynamics in atoms driven by near-infrared and mid-infrared laser pulses. 2) Explore effects due to the magnetic field of light in correlated two and three-electron escape during ionization in atoms as well as in two and three-center molecules driven by near-infrared and mid-infrared laser pulses that are either linearly or elliptically polarized or by vector beams, i.e. "twisted" laser fields, an intriguing form of light that twists like a helical corkscrew. 3) Control correlated multi-electron ionization and the formation of highly exited Rydberg states in four-active-electron three-center molecules by employing two-color laser fields or vector beams.

The quest for improved energy storage is currently one of the most important scientific challenges. The UK is investing heavily in energy storage and renewable energy technologies and is committed to reducing its CO2 emissions by replacing the majority of its electricity generating capacity over the next few decades. Building better batteries is key to the use of electricity in a low-carbon future and for the exploitation of current and next-generation technologies. Current Li-ion batteries based on liquid electrolytes cannot meet the requirements of future applications. The creation of safer, cheaper, recyclable and higher energy density batteries is therefore essential for the electrification of transport and grid-scale storage of energy from renewable resources. This EPSRC New Investigator Award will develop transformative methods that will deliver solutions to these societally and industrially critical problems. Solid-state Li-ion batteries are a rapidly emerging technology with the potential to revolutionise energy storage. This technology utilises solid electrolytes instead of the flammable liquid electrolytes found in current Li-ion batteries. The solid-state architecture has the potential to significantly increase both the safety and energy density of next-generation batteries. Their performance is, however, currently limited by a number of underlying challenges, including the presence of highly resistive interfaces and difficulties in controlling the microstructures of the solid electrolytes that these batteries are built around. These challenges greatly hinder Li-ion transport and are therefore highly detrimental to the operation of the battery. To address these pertinent issues, the team will develop and apply state-of-the-art computational and experimental techniques to provide a fundamental understanding of ion transport at the microscale of solid electrolytes for solid-state batteries. Such an understanding will allow for the design of solid electrolyte microstructures that promote Li-ion transport instead of restricting it. The insights obtained for solid-state batteries in this project will also have direct implications for other battery and energy technologies where the microstructure and solid-solid interfaces again play crucial roles in determining their performance.

The ability to accurately measure the power and frequency (or wavelength) distribution of an optical signal is crucial to a vast range of applications, for spectroscopy in medicine, ensuring the safety of food or pharmaceuticals to remote sensing of gasses and fundamental science, e.g. characterising short laser pulses or finding the atmospheres of extrasolar planets. Currently, this is achieved using Optical Spectrum analyzers or optical monochromators, which have a key limitation. To achieve high-resolution they need a large optical path length and therefore large footprint (optical path length on the order of 0.5-1 m is common). Thus these devices are bulky and expensive. While not an issue for lab-based low-volume applications, this excludes their use - and thus the use of high-resolution spectroscopy - in large volume, or footprint and weight-sensitive applications, e.g. integration into lab-on-a-chip devices, mobile phones and low mass satellites (e.g. cube-sat). These applications can only be served by integrated on-chip spectrometers. Here the use of speckle spectrometers, using the random scattering of light to achieve a high wavelength resolution in an ultra-small footprint would be highly promising if it were not for the case that typical the multiple scattering needed to create the speckle results in most of the light being scattered out of the device before it can be detected. However, over the last decade, several groups (including myself) have shown that the statistical distribution of scattering sites can be used to control the amount and direction (e.g. within the plane of the device vs out-of-plane) of light scattering. In this project we merge these advances with speckle spectrometers, i.e. using controlled disorder to efficiently generate a speckle pattern, while virtually eliminating out-of-plane scattering and optical losses. Building on this advance we will demonstrate a high resolution, low footprint on-chip spectrometer that outperforms the state of the art by orders of magnitude (in device footprint) without sacrificing the device resolution. We will also demonstrate that these devices are suitable for future large scale manufacturing, using pre-existing CMOS facilities, are suitable for gas spectroscopy and laser pulse spectrum analysis and compatible with future integration with optical detectors for a direct electronic readout. This would present a game-changing advance in the field of integrated spectrometers and lay the foundation for future commercialization of integrated speckle spectrometers.