Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.

This is mathematical research connecting the analysis of partial differential equations (PDEs) and (applied) probability. The main goal of this project is to derive macroscopic evolution laws for interfaces in heterogeneous, random environments, described on a small scale by nonlinear PDEs with random coefficients. In particular, we want to go beyond classical homogenisation in order to treat systems where a long-range collective behaviour emerges. A key aspect of this project is to establish a new link between analysis and probability, benefitting both fields, by working on problems motivated by applications. It is motivated by the following situation: With an interface is associated a scalar quantity called its energy (think e.g. of its area) which it tries to decrease, i.e., it performs a gradient flow. This energy is perturbed through obstacles or impurities on a very small scale, and driven by some large-scale force. The impurities are random, i.e., we have information only on the probability of finding certain impurities in a certain place, not on their precise nature and location. We are interested in the effective velocity and other qualitative properties of the interface on a large scale, much larger than the scale on which the perturbations vary. On that scale, the perturbations should average out, but the questions is: What is the effective evolution law on a large scale, and what are the qualitative properties of the interface, e.g. on which scales does it look rough due to all the random heterogeneities? How does all this depend on the law of the impurities? This is important because we are interested in the reaction of a system on the scale of our everyday life to an input on that scale. E.g. we would like to know how a piece of metal changes shape in a car crash, we are not interested in the position of each single atom, and we wouldn't be able to compute those anyway. But most realistic materials have some random structure on a fine scale.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

We are currently facing an unprecedented climate emergency threatening life on our planet. Limiting global surface temperature rise is key to ensure irreversible effects for nature and people are not triggered. For the UK, decarbonisation of the energy sector to mitigate climate change is a crucial ambition, becoming the first major economy to pass legislation to end its contribution to global warming by 2050 by reducing its carbon emissions to net-zero. Even though a significant emission reduction has been already achieved in the electric power sector, progress has been limited in other areas, such as heating (including space cooling), which accounts for over a third of UK emissions. Heating and cooling are central to our lives not only for comfort and daily activities, but also to facilitate productive workplaces and to run a variety of industrial processes. Decarbonising heating and cooling and reducing emissions from buildings are thus paramount to meet net-zero targets. Cooling decarbonisation has not previously received significant attention, but this is changing due to population increase and climate change. Summertime cooling of buildings is becoming increasingly important and consumer demand for greater comfort levels will also increase the energy used for cooling services. An increased requirement for cooling is anticipated, with the share of UK electricity used for cooling also expected to rise further, which could strain the electricity system. At the same time, summer electricity demand is changing with a surge in solar PV generation, causing concern for balancing the power system. Since cooling facilities are in general limited to building level, significant investments in cooling infrastructure and buildings are needed. Flex-Cool-Store brings together academics with complementary expertise on techno-economic, societal and policy aspects of electrical power supply and thermal energy systems. The main objective of this interdisciplinary project is to investigate the potential impacts of a growth in UK cooling demand and how this growth can be managed through proactive design and flexible operation of the cooling supply system and energy storage, and how the new demand can be served by an increasingly decarbonised electricity system. Underpinning this, public perception towards the adoption of cooling technologies within buildings and communities and consumer participation in flexibility provision from energy storage at household level will be explored via interviews and public workshops. Outcomes will be considered alongside pathways and policies associated with heat decarbonisation, and novel analysis using 'elite' interviews with policy makers will be conducted to consider the potential relationship between heat decarbonisation strategies, cooling and storage. This interdisciplinary approach will enable Flex-Cool-Store to address the issue of increasing demand for cooling and decarbonisation from multiple angles and to develop an even stronger evidence for best practice around buildings decarbonisation. Specific objectives of the project are: 1. Understanding cooling demand considering technical and socio-economic factors. Detailed studies will be conducted to understand how cooling demand might change over the next decades. 2. Quantifying the impacts of increased cooling demand on electricity networks. The extent to which supplying cooling will affect peak electricity demand will be quantified and its implications on network reinforcement will be investigated for selected case studies using data from real practical projects. 3. Investigating the flexibility provision to the electrical power system from integrating cooling technologies and storage. The interactions and synergies between cooling and electricity systems will be studied. How to adopt a coordinated approach for designing and operating energy systems of buildings so that the provision of flexibility can be maximised will be explored.

8.75M people in the UK have sought treatment for osteoarthritis (OA) and the condition costs the UK economy £10B/year (Versus Arthritis). Current treatments only alleviate the symptoms or potentially delay progression. To quantify the efficacy of future therapeutics, accurate evaluation of normal and pathological in-vivo knee joint function (movement and loading) are essential. Traditionally, computational modelling of knee loading relies on marker-based motion capture as input data, creating inaccuracies in the contact dynamics due to soft tissue errors associated with markers attached to the skin. As an innovative response to this limitation, Dynamic Biplane X-Ray imaging (DBX), developed at Cardiff, captures real-time moving images of a volunteer's knee joint during activity. For this studentship, DBX, in combination with high fidelity Magnetic Resonance Imaging (MRI) will provide highly-accurate, subject-specific input data to develop more realistic dynamic musculoskeletal and contact models with associated estimates of tissue loading in healthy and osteoarthritic knees. This unique interdisciplinary project will integrate existing imaging, experimental and computational technologies into a novel multi-scale modelling framework with the aim to: - Provide a subject-specific knee modelling framework accounting for movement, loading, anatomy and muscle activity - Calibrate a knee cartilage model accounting for control and OA cartilage properties using DBX and MRI data - Validate the multi-scale model using in-vivo data for healthy and OA volunteers Based on the robust modelling framework developed during the studentship, early surgical and non-surgical therapeutics aiming to normalise the knee's mechanical environment can then be explored.