This Centre for Doctoral training in Industrially Focused Mathematical Modelling will train the next generation of applied mathematicians to fill critical roles in industry and academia. Complex industrial problems can often be addressed, understood, and mitigated by applying modern quantitative methods. To effectively and efficiently apply these techniques requires talented mathematicians with well-practised problem-solving skills. They need to have a very strong grasp of the mathematical approaches that might need to be brought to bear, have a breadth of understanding of how to convert complex practical problems into relevant abstract mathematical forms, have knowledge and skills to solve the resulting mathematical problems efficiently and accurately, and have a wide experience of how to communicate and interact in a multidisciplinary environment. This CDT has been designed by academics in close collaboration with industrialists from many different sectors. Our 35 current CDT industrial partners cover the sectors of: consumer products (Sharp), defence (Selex, Thales), communications (BT, Vodafone), energy (Amec, BP, Camlin, Culham, DuPont, GE Energy, Infineum, Schlumberger x2, VerdErg), filtration (Pall Corp), finance (HSBC, Lloyds TSB), food and beverage (Nestle, Mondelez), healthcare (e-therapeutics, Lein Applied Diagnostics, Oxford Instruments, Siemens, Solitonik), manufacturing (Elkem, Saint Gobain), retail (dunnhumby), and software (Amazon, cd-adapco, IBM, NAG, NVIDIA), along with two consultancy companies (PA Consulting, Tessella) and we are in active discussion with other companies to grow our partner base. Our partners have five key roles: (i) they help guide and steer the centre by participating in an Industrial Engagement Committee, (ii) they deliver a substantial elements of the training and provide a broad exposure for the cohorts, (iii) they provide current challenges for our students to tackle for their doctoral research, iv) they give a very wide experience and perspective of possible applications and sectors thereby making the students highly flexible and extremely attractive to employers, and v) they provide significant funding for the CDT activities. Each cohort will learn how to apply appropriate mathematical techniques to a wide range of industrial problems in a highly interactive environment. In year one, the students will be trained in mathematical skills spanning continuum and discrete modelling, and scientific computing, closely integrated with practical applications and problem solving. The experience of addressing industrial problems and understanding their context will be further enhanced by periods where our partners will deliver a broad range of relevant material. Students will undertake two industrially focused mini-projects, one from an academic perspective and the other immersed in a partner organisation. Each student will then embark on their doctoral research project which will allow them to hone their skills and techniques while tackling a practical industrial challenge. The resulting doctoral students will be highly sought after; by industry for their flexible and quantitative abilities that will help them gain a competitive edge, and by universities to allow cutting-edge mathematical research to be motivated by practical problems and be readily exploitable.

This proposal is for a Doctoral Training Centre to provide a new generation of engineering leaders in Offshore & Marine Renewable Energy Structures. This is a unique opportunity for two internationally leading Universities to join together to provide an industrially-focussed centre of excellence in this pivotal subject area. The majority of informed and balanced views suggest approximately 180 TWh/year of offshore wind, ~300km of wave farms (19 TWh/year), 1,000 tidal stream turbines (6 TWh/year) and 3 small tidal range schemes (3 TWh/year) are desirable/achievable using David MacKay's UK DECC 2050 Pathways calculator. These together would represent 30% of predicted actual UK electricity demand. This would be a truly enormous renewable energy contribution to the UK electricity supply, given the predicted increase of electricity demand in the transport sector. The inclusion of onshore wind brings this figure closer to 38% of UK electricity by 2050. RenewablesUK predicts Britain has the opportunity to lead the world in developing the emerging marine energy industry with the sector having the potential to employ 10,000 people and generate revenues of nearly £4bn per year by 2020. The large scale development of offshore renewable energy (Wind, Wave and Tidal) represents one of the biggest opportunities for sustainable economic growth in the UK for a generation. The emerging offshore wind sector is however unlike the Oil & Gas industry in that structures are unmanned, fabricated in much larger volumes and the commercial reality is that the sector has to proactively take measures to further reduce CAPEX and OPEX. Support structures need to be structurally optimised and to avail of contemporary and emerging methodologies in structural integrity design and assessment. Current offshore design standards and practices are based on Offshore Oil & Gas experience which relates to unrepresentative target structural reliability, machine and structural loading characteristics and scaling issues particularly with respect to large diameter piled structural systems. To date Universities and the Industry have done a tremendous job to help device developers test and trial different concepts however the challenge now moves to the next stage to ensure these technologies can be manufactured in volume and deployed at the right cost including installation and maintenance over the full design life. This is a proposal to marry together Marine and Offshore Structures expertise with emerging large steel fabrication and welding/joining technologies to ensure graduates from the programme will have the prerequisite knowledge and experience of integrated structural systems to support the developing Offshore and Marine Renewable Energy sector. The Renewable Energy Marine Structures (REMS) Doctoral Centre CDT will embrace the full spectrum of Structural Analysis in the Marine Environment, Materials and Engineering Structural Integrity, Geotechnical Engineering, Foundation Design, Site Investigation, Soil-Structure Interaction, Inspection, Monitoring and NDT through to Environmental Impact and Quantitative Risk and Reliability Analysis so that the UK can lead the world-wide development of a new generation of marine structures and support systems for renewable energy. The Cranfield-Oxford partnership brings together an unrivalled team of internationally leading expertise in the design, manufacture, operation and maintenance of offshore structural systems and together with the industrial partnerships forged as part of this bid promises a truly world-leading centre in Marine Structures for the 21st Century.

EPSRC Centre for Doctoral Training in Resilient Decarbonised Fuel Energy Systems Led by the University of Nottingham, with Sheffield and Cardiff SUMMARY This Centre is designed to support the UK energy sector at a time of fundamental change. The UK needs a knowledgeable but flexible workforce to deliver against this uncertain future. Our vision is to develop a world-leading CDT, delivering research leaders with broad economic, societal and contextual awareness, having excellent technical skills and capable of operating in multi-disciplinary teams covering a range of roles. The Centre builds on a heritage of two successful predecessor CDTs but adds significant new capabilities to meet research needs which are now fundamentally different. Over 80% of our graduates to date have entered high-quality jobs in energy-related industry or academe, showing a demand for the highly trained yet flexible graduates we produce. National Need for a Centre The need for a Centre is demonstrated by both industry pull and by government strategic thinking. More than forty industrial and government organisations have been consulted in the shaping and preparation of this proposal. The bid is strongly aligned with EPSRC's Priority Area 5 (Energy Resilience through Security, Integration, Demand Management and Decarbonisation) and government policy. Working with our partners, we have identified the following priority research themes. They have a unifying vision of re-purposing and re-using existing energy infrastructure to deliver rapid and cost-effective decarbonisation. 1. Allowing the re-use and development of existing processes to generate energy and co-products from low-carbon biomass and waste fuels, and to maximise the social, environmental and economic benefits for the UK from this transition 2. Decreasing CO2 emissions from industrial processes by implementation of CCUS, integrating with heat networks where appropriate. 3. Assessing options for the decarbonisation of natural gas users (as fuel or feedstock) in the power generation, industry and domestic heating system through a combination of hydrogen enhancement and/or CO2 capture. Also critical in this theme is the development of technologies that enable the sustainable supply of carbon-lean H2 and the adoption of H2 or H2 enriched fuel/feedstock in various applications. 4. Automating existing electricity, gas and other vector infrastructure (including existing and new methods of energy storage) based on advanced control technologies, data-mining and development of novel instrumentation, ensuring a smarter, more flexible energy system at lower cost. Training Our current Centre operates a training programme branded 'exemplary' by our external examiner and our intention is to use this as solid basis for further improvements which will include a new technical core module, a module on risk management and enhanced training in inclusivity and responsible research. Equality, Diversity and Inclusion Our current statistics on gender balance and disability are better than the EPSRC mean. We will seek to further improve this record. We are also keen to demonstrate ED&I within the Centre staff and our team also reflects a diversity in gender, ethnicity and experience. Management and Governance Our PI has joined us after a career conducting and managing energy research for a major energy company and led development of technologies from benchtop to full-scale implementation. He sharpens our industrial focus and enhances an already excellent team with a track record of research delivery. One Co-I chairs the UoN Ethics Committee, ensuring that Responsible Innovation remains a priority. Value for Money Because most of the Centre infrastructure and organisation is already in place, start-up costs for the new centre will be minimal giving the benefit of giving a new, highly refreshed technical capability but with a very low organisational on-cost.

The main focus of this project is to experimentally investigate and mathematically describe emergent properties of a large cellular system. A large cellular population is a complex dynamical system far from equilibrium, where macro-dynamics are driven by interactions and heterogeneity at the systems micro- or cell-level. Understanding exactly how microstate properties instigate and perpetuate emergent macroscopic phenomena is one of the fundamental challenges facing contemporary biology today. Quantifying such symbiotic relationships is at the heart of many scientific research endeavours. This broad scientific area covers an equally matched myriad of length scales, ranging from spontaneous symmetry breaking at the sub-atomic level through to galactic cluster formation at the cosmic scale. For the most part, formations of emergent configurations in these systems are intrinsically linked to non-linear interactions between the individual components that together constitute the complex system. It has been established that many of the confounding features of such systems can be adequately described through the application of statistical mechanics. The mathematical methodology can encapsulate and link macroscopic descriptions of the system to that of the microstate, allowing emergent ensemble behaviours to be quantified. Large cellular populations fulfil all necessary criteria to be considered a complex system (i.e. the cell being the systems microstate); constituent cells are vast number; cells are heterogeneous in physical, biological function; cell-cell and cell-environment interactions are inherently nonlinear. Adherence of the microstates to these criteria promotes the formation of emergent behaviour at the cellular population level; significant examples include embryo development, tissue regeneration during wound healing and the proliferation of metastatic diseases. However, application of statistical mechanics to describe and predict large-scale cellular systems have been hampered due to the fact that (i) such systems are in a state of non-equilibrium exhibiting vast heterogeneity across constituent microstates, simply averaging over ensemble variability results in distorted macroscopic system view and (ii) the ability to identify, track and quantify significant numbers of individuals within a cellular population to assess and account for microstate variability has been hindered by the availability of high-throughput microscopy platforms. Together these issues have obstructed application of statistical mechanics methods to elucidate upon the formation, function and stability of ensemble behaviour of a complex cellular system. The work presented as part of this EPSRC first grant application will address this current shortfall in scientific application and understanding. Recent advances in high-throughput microscopy present an opportunity to collate detailed information of microstate behaviour and allow development of mathematical models to describe the system. This interdisciplinary proposal seeks to unify contemporary biology, advanced imaging and statistical mathematics in order to measure and track the evolving interactions, dynamics and fate of >100,000 individual cells over extended periods. This databank will provide invaluable information, detailing microstate quantities such as morphology, biological function and spatial correlation and will further allow realisation of stochastic and master equation descriptions of the large-scale cellular system in question. Furthermore, this will ensure system variability is incorporated within models at the outset, providing robust linkage between the systems micro- to macro-levels and allowing sources of emergent phenomena to be more accurately described and predicted.

Decarbonising both heating and cooling across residential, business and industry sectors is fundamental to delivering the recently announced net-zero greenhouse gas emissions targets. Such a monumental change to this sector can only be delivered through the collective advancement of science, engineering and technology combined with prudent planning, demand management and effective policy. The aim of the proposed H+C Zero Network will be to facilitate this through funded workshops, conferences and secondments which in combination will enable researchers, technology developers, managers, policymakers and funders to come together to share their progress, new knowledge and experiences. It will also directly impact on this through a series of research funding calls which will offer seed funding to address key technical, economic, social, environmental and policy challenges. The proposed Network will focus on the following five themes which are essential for decarbonising heating and cooling effectively: Theme 1 Primary engineering technologies and systems for decarbonisation Theme 2 Underpinning technologies, materials, control, retrofit and infrastructure Theme 3 Future energy systems and economics Theme 4 Social impact and end users' perspectives Theme 5 Policy Support and leadership for the transition to net-zero