The advancement of numerous technologies has become increasingly reliant on the ability to dissipate large quantities of heat from small areas. Current designs in power electronics, supercomputers, lasers, X-ray medical devices, nuclear fusion reactor blankets, spacecraft, and hybrid vehicle electronics, and future improvements, rely on record high heat transfer rates. This rapid increase in heat dissipation rates required by such devices has led to a transition from more traditional fan-cooled heat-sink attachments to liquid cooling techniques. Liquid cooling techniques operating in single-phase, however, have now reached their limit being forced to run at very low inlet temperatures and exceedingly high mass flow rates, resulting in unacceptably high pressure drops and surface temperature gradients. Innovative approaches are urgently needed to overcome these significant shortcomings: one such approach is spray-cooling. Spray-cooling uses a nozzle to break up the liquid coolant into fine droplets that impinge individually on a heated surface. 'Low'- and 'high-temperature' spray-cooling applications involve surface temperatures below and above the critical heat flux (CHF), respectively. Single-phase spray-cooling (relies on liquid sensible heat rise only) provides greater operational stability and spatially uniform heat removal than liquid cooling, reducing the likelihood of large surface thermal gradients, particularly important for fragile electronic components. Two-phase spray-cooling (relies on liquid sensible heat rise and latent heat), are superior to single-phase systems and furthermore, compared to pool/flow boiling alternative systems, offer far less resistance to vapour removal from a heated surface enabling superior drop-surface contact . In fact, the CHF increases from 1.2 MW/m2 (for water pool boiling) to 10 MW/m2 for water sprays in two-phase applications. SANGRIA is an ambitious 3-year collaborative research programme aimed at investigating the fundamental mechanisms and transfer processes underlying spray-cooling. This project combines cutting-edge experimental techniques that furnish spatiotemporally-resolved diagnostics of the thermal, interfacial, and hydrodynamic fields, with multi-scale theory, modelling and 3-D high-fidelity numerical simulation that bridge the molecular and continuum-scales. The deep insights generated from SANGRIA will be harnessed to provide tools that are practically implementable by our industrial partners in order to maximise impact. Industrial and academic partners will provide additional technical support and feedback during the research programme plus pathways for direct industrial impact. The industrial partners include possible users of this technology: TMD Ltd (manufacturers of electronic equipment, high heat flux devices); Oxford naNosystems (manufacturers of enhanced heat transfer surfaces); ANSYS (Software development); Siemens (Software development); Spraying Systems Co. (Nozzle manufacturers); Syngenta (users of nozzles). LaVision offered a 15% discount on their Particle Master System. The academic partners from the University of Nottingham, Sorbonne University, Technical University of Darmstadt and Kyushu University are internationally recognised experts in single and two-phase thermal systems, including spray cooling. Participation and presentations during the HEXAG and PIN meetings will facilitate feedback and technology transfer.

The job of materials science is to develop the materials that we need to make all of the things that we rely on in our daily lives. These range from the materials used to make large scale objects, such as aeroplanes and buildings, right down to the smallest scales like the processors in the electronic devices we use every day. These materials are often complicated and need to be carefully designed with just the right properties needed to do their jobs for many decades and often in incredibly harsh conditions. There are many current challenges that require us to develop new, improved materials. We need to meet our net-zero climate goals and get better at designing products that can be fully recycled, for example. And there are some resources that we currently use in important materials for which we would like to find alternatives. These are difficult challenges and we need to overcome them quickly. But the way that materials scientists have worked to develop a new material in the past is too slow: it can take up to 20 years to develop a new material and we cannot wait that long. Fortunately, recent developments in the computer simulation of materials, in robotics and sensor technology, in our ability to exploit large volumes of data through machine learning and in techniques for quickly making and testing large numbers of different materials can help to speed things up. This idea, bringing digital technologies together to help us make better materials more quickly, is called "Materials 4.0". If we are going to take advantage of Materials 4.0 then we need to make sure that materials scientists have the necessary digital skills. These skills, things like data informatics, machine learning and advanced computer simulation, are not usually covered in depth in undergraduate university courses in science and engineering. So, the Henry Royce Institute, the UK's national institute for advanced materials, in partnership with the National Physical Laboratory, is proposing to set up a Centre for Doctoral Training (CDT) that will take at least 70 science and engineering graduates and train them in the techniques of Materials 4.0. These students will work towards PhDs and become leaders in the field of Materials 4.0. They will undertake research projects in universities across the UK (Cambridge, Oxford, Imperial College, Manchester, Sheffield, Leeds and Strathclyde), tackling a broad range of materials science challenges and developing new approaches in Materials 4.0. The need for these new approaches is widespread, throughout academia and in industry. In recognition of this, the training programme that we develop for the CDT will be made available more widely, in different forms, so that we can disseminate skills in Materials 4.0 to existing researchers in universities and industrial companies as quickly as possible. The training approach of the CDT will be to take our students from "Learners to Leaders" over the course of four years. Our students will be working across boundaries between materials science and computer / data science and between academia and industry. They will build new interfaces and help to develop a common language for communication. To strengthen our students' own learning and to disseminate their skills more widely, we will train our students as trainers so that the students are actively involved in designing and delivering training for fellow researchers and take the role of ambassadors for a cultural shift in materials science to modern ways of working.

Uncertainty is ubiquitous in the mathematical characterisation of engineered and natural systems. In many structural engineering applications, a deterministic characterisation of the response may not be realistic because of uncertainty in the material constitutive laws, operating conditions, geometric variability, unmodelled behaviour, etc. Ignoring these sources of uncertainties or attempting to lump them into a factor of safety is no longer widely considered to be a rational approach, especially for high-performance and safety-critical applications. It is now increasingly acknowledged that modern computational methods must explicitly account for uncertainty and produce a certificate of response variability alongside nominal predictions. Advances in this area are key to bringing closer the promise of computational models as reliable surrogates of reality. This capability will potentially allow significant reductions in the engineering product development cycle due to decreased reliance on extensive experimental testing programs and enable the design of systems that perform robustly in the face of uncertainty. The proposed investigation will address this important research problem and deliver convergent computational methods and efficient software implementations that are orders of magnitude faster than direct Monte-Carlo simulation for predicting the response of structural systems in the presence of uncertainty. This work will draw upon developments in stochastic subspace projection theory which have recently emerged as a highly efficient and accurate alternative to existing techniques in computational stochastic mechanics. The overall objectives of this project include: (1) formulation of convergent stochastic projection schemes for predicting the static and (low and medium frequency) dynamic response statistics of large-scale stochastic structural systems. (2) design and implementation of a state-of-the-art parallel software framework that leverages existing deterministic finite element codes for stochastic analysis of complex structural systems, and (3) laboratory and computer experiments to validate the methods developed. The methods to be developed will find applications to a wide range of structural problems that require efficient and accurate predictions of performance and safety in the presence of uncertainty. This is a crucial first step towards rational design and control strategies that can meet stringent performance targets and simultaneously ensure system robustness. Progress in this area would also be of benefit to many other fields in engineering and the physical sciences where there is a pressing need to quantify uncertainty in predictive models based on partial differential equations.

The Transforming the Foundation Industries Challenge has set out the background of the six foundation industries; cement, ceramics, chemicals, glass, metals and paper, which produce 28 Mt pa (75% of all materials in our economy) with a value of £52Bn but also create 10% of UK CO2 emissions. These materials industries are the root of all supply chains providing fundamental products into the industrial sector, often in vertically-integrated fashion. They have a number of common factors: they are water, resource and energy-intensive, often needing high temperature processing; they share processes such as grinding, heating and cooling; they produce high-volume, often pernicious waste streams, including heat; and they have low profit margins, making them vulnerable to energy cost changes and to foreign competition. Our Vision is to build a proactive, multidisciplinary research and practice driven Research and Innovation Hub that optimises the flows of all resources within and between the FIs. The Hub will work with communities where the industries are located to assist the UK in achieving its Net Zero 2050 targets, and transform these industries into modern manufactories which are non-polluting, resource efficient and attractive places to be employed. TransFIRe is a consortium of 20 investigators from 12 institutions, 49 companies and 14 NGO and government organisations related to the sectors, with expertise across the FIs as well as energy mapping, life cycle and sustainability, industrial symbiosis, computer science, AI and digital manufacturing, management, social science and technology transfer. TransFIRe will initially focus on three major challenges: 1 Transferring best practice - applying "Gentani": Across the FIs there are many processes that are similar, e.g. comminution, granulation, drying, cooling, heat exchange, materials transportation and handling. Using the philosophy Gentani (minimum resource needed to carry out a process) this research would benchmark and identify best practices considering resource efficiencies (energy, water etc.) and environmental impacts (dust, emissions etc.) across sectors and share information horizontally. 2 Where there's muck there's brass - creating new materials and process opportunities. Key to the transformation of our Foundation Industries will be development of smart, new materials and processes that enable cheaper, lower-energy and lower-carbon products. Through supporting a combination of fundamental research and focused technology development, the Hub will directly address these needs. For example, all sectors have material waste streams that could be used as raw materials for other sectors in the industrial landscape with little or no further processing. There is great potential to add more value by "upcycling" waste by further processes to develop new materials and alternative by-products from innovative processing technologies with less environmental impact. This requires novel industrial symbioses and relationships, sustainable and circular business models and governance arrangements. 3 Working with communities - co-development of new business and social enterprises. Large volumes of warm air and water are produced across the sectors, providing opportunities for low grade energy capture. Collaboratively with communities around FIs, we will identify the potential for co-located initiatives (district heating, market gardening etc.). This research will highlight issues of equality, diversity and inclusiveness, investigating the potential from societal, environmental, technical, business and governance perspectives. Added value to the project comes from the £3.5 M in-kind support of materials and equipment and use of manufacturing sites for real-life testing as well as a number of linked and aligned PhDs/EngDs from HEIs and partners This in-kind support will offer even greater return on investment and strongly embed the findings and operationalise them within the sector.

Meeting emerging science and engineering modelling challenges requires scientists who can master complex theory and simulation techniques, can assimilate data, and can collaborate in multidisciplinary teams with expertise across a range of modelling scales. Securing the UK's position as a world-leading research hub into the future therefore requires a well-integrated pool of researchers with a skillset that is both broad and deep. HetSys is leading the way in addressing these needs by producing students with the tools necessary to meet the challenges of the future through our training programme. We are training the scientists who will develop the next generation of computational models, implemented in reusable software with robust error bars from uncertainty quantification (UQ), and who can learn from experimental and simulated data on an equal footing through advances in 'scientific machine-learning' (SciML). Linking heterogeneous materials models with UQ allows performance to be improved, enabling the technology needed to reach net zero through a step-change in design capability. The ongoing AI revolution has necessitated a redesign of our training programme to enable us to build on what we learnt during the first funding period and deliver our new vision. In particular, changes to our core training enable our students to (i) embed robust and sustainable research software engineering (RSE) in modelling; (ii) quantify modelling uncertainties through enhanced use of statistical methods; and (iii) exploit new trends in scientific machine learning. The research focus of HetSys on new paradigms in the behaviour of heterogeneous materials remains vital for the competitiveness of the UK's high-value manufacturing and automotive industries. Prominent examples of challenges we are addressing include the design of (i) energy materials for future vehicles with reduced carbon footprints; (ii) low dimensional and/or strongly correlated materials for quantum devices; (iii) high entropy alloys for fusion applications; (iv) biomolecules for combatting infectious diseases. Historically, the modelling pattern has focused on just one length- or time-scale; HetSys transforms this landscape by explicitly targeting the multiscale modelling of heterogeneous systems required by industry. The expertise we have accumulated opens up opportunities to capitalise on the transformative combination of mechanistic modelling with data-driven approaches (SciML). This requires a broader combination of disciplinary expertise, provided through our enhanced bespoke training programme. Only a cohort approach can train high-quality computational scientists who can develop and implement new modelling methods in close collaboration with other scientists. The cohesive, interdepartmental cohorts and training programme we are creating lower many of the current barriers to interdisciplinary work and demonstrate our vision for the future of scientific endeavour, where teams of researchers work together to combine their skills and expertise. Only a critical mass of students and a large and highly collaborative team of supervisors makes this targeted and fully inclusive training approach feasible. HetSys supports the delivery of EPSRC's Physical and Mathematical Sciences Powerhouse strategic priority, helping to provide the platform on which research and innovation across the sciences is built.