Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow (together with a 'kinetic under-cooling' regularisation) where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We perform linear stability analysis and derive a diffuse-interface approximation of the model. Finiteelement discretisations of two closely related models are presented, together with computational results comparing the approximate solutions.

This work presents eight demonstrators and one showcase developed within the 5G-Xcast project. They experimentally demonstrate and validate key technical enablers for the future of media delivery, associated with multicast and broadcast communication capabilities in 5 th Generation (5G). In 5G-Xcast, three existing testbeds: IRT in Munich (Germany), 5GIC in Surrey (UK), and TUAS in Turku (Finland), have been developed into 5G broadcast and multicast testing networks, which enables us to demonstrate our vision of a converged 5G infrastructure with fixed and mobile accesses and terrestrial broadcast, delivering immersive audiovisual media content. Built upon the improved testing networks, the demonstrators and showcase developed in 5G-Xcast show the impact of the technology developed in the project. Our demonstrations predominantly cover use cases belonging to two verticals: Media & Entertainment and Public Warning, which are future 5G scenarios relevant to multicast and broadcast delivery. In this paper, we present the development of these demonstrators, the showcase, and the testbeds. We also provide key findings from the experiments and demonstrations, which not only validate the technical solutions developed in the project, but also illustrate the potential technical impact of these solutions for broadcasters, content providers, operators, and other industries interested in the future immersive media delivery.

<p>Surface transport forecasting has traditionally focused on deterministically categorising the state - for example, dry, damp, or icy - of a road surface, to provide decision support to winter gritting services. However, with the emerging Connected Autonomous Vehicle (CAV) sector, the ability to accurately describe a broader range of weather conditions, at a much smaller temporal and spatial scale, is becoming equally important to ensuring public safety. Localised conditions such as road spray, rain and fog can all degrade the performance of CAV sensors, whilst settled snow also has the potential to impede navigation by obscuring road markings. The difficulty of deterministically forecasting such precise localised conditions requires us to quantify uncertainty, driving a move towards probabilistic, risk-based forecasting. Therefore, the Met Office is currently developing a new Surface Transport Forecasting (STF) post-processing system, designed to accommodate these future user requirements.</p><p>The new STF post-processing system is centred on the Joint UK Land Environment System (JULES); a community model used as the land-surface component of the Met Office Unified Model (UM), but which can also be used – as we do here – as a stand-alone land-surface model driven by forecast output from Numerical Weather Prediction (NWP) models. To produce probabilistic forecasts for locations within the United Kingdom, we are using output from the Met Office regional ensemble model MOGREPS-UK to drive JULES. MOGREPS-UK is a 2.2km resolution 18-member ensemble which provides forecasts out to 5 days. It is generated by time-lagging over 6 hours, initialising three new ensemble members every hour from perturbed initial conditions. By running JULES for each ensemble member, we create a set of possible road forecast outputs. Considering these predictions in aggregate allows us to generate probabilistic forecasts of road weather conditions.</p><p>Our ensemble-driven STF system has been verified using standard ensemble verification techniques, including rank histograms and reliability plots. Initial analysis of results, using data from approximately 300 locations in the United Kingdom for which good quality road weather observations are available between 2015 and 2021, indicate that observed road surface states are generally captured within the spread of predictions. The new system has been compared with the current deterministic STF system.  In particular, in challenging meteorological conditions (for example, where there is variable cloud cover, scattered showers, or on marginal temperature nights) the probabilistic approach allows us to quantify the uncertainty in the road state forecast in a way that the deterministic approach does not. Further work will focus on the most effective way to communicate probabilistic forecasts to end-users, ensuring they are able to apply the output to enhance their decision-making.</p>

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Since the 1980s the Met Office has produced Surface Transport Forecasts (STF) for the UK. These forecasts allow mitigation of the UK surface transport infrastructure’s vulnerability to weather-based impacts across the autumn and winter season, for example road ice (roads are gritted during ice events), and low rail adhesion (the speed of trains is adapted). Although historically sufficient, these forecasts have limitations, such as not accurately forecasting high summer maximum temperatures, which are becoming more common due to the changing climate. These high temperatures lead to melting road surfaces and buckling railway lines. The current STF system additionally struggles with the future needs of Connected Autonomous Vehicles, for example hazards which specifically impact the on-board sensors such as road spray, and flexible machine-machine communication. In order to address the limitations of the current STF system, the Met Office is building a new system. This is both a refresh of the pipeline, with a goal to make it flexible, robust, and portable, as well as a revisit of the scientific code within. Updates to the scientific core centre around upgrading the physics model to the Joint UK Land Environment Simulator (JULES). This allows us to accurately capture summer maximum temperatures and carefully model the depth of water on the road (vital for a road spray forecast). Other scientific updates include using Machine Learning based approaches for bias correction and the spin up of new forecast locations (necessary for delivering the service via an API), and building probabilistic ensemble-based forecasts. The physics model JULES is a community model used as the land-surface component of the Met Office’s Unified Model, but which can also be used – as we do here – as a stand-alone surface-exchange-scheme driven by forecast output from Numerical Weather Prediction models. JULES models a comprehensive list of physical land-surface energy processes, as well as modelling water and snow stores. We have extended JULES to better capture processes specific to a road. Externally to JULES we have implemented a shading scheme and heating due to longwave radiation emitted by traffic.

Continuous welded rails, which are used as standard on the United Kingdom railway network, are optimised to withstand a specified temperature range centred around a given “stress-free temperature” (SFT). This is the temperature at which the rail is neither in tension nor compression. Higher SFTs mean the track can withstand higher temperatures before expanding. However, too high an SFT makes the rail susceptible to brittleness and cracks in low winter temperatures. Exceeding the temperature range within which the rail is designed to operate can cause it to distort, leading to increased instances of buckling. Although rare, derailment caused by buckling can result in catastrophic consequences. Therefore, to prevent such accidents, blanket speed restrictions are currently imposed when the forecast air temperature exceeds a set threshold. However, these blanket speed restrictions are based on the simple assumption that the rail surface temperature will be a constant value above the air temperature. This assumption is widely adopted even though observations show that rail surface temperature is not linearly correlated with air temperature. If rail surface temperatures can be accurately and reliably modelled, speeds restrictions and preventative measures can be more targeted. This is becoming increasingly important since climate change is predicted to increase the frequency of occurrence of extreme high temperatures in the United Kingdom. Therefore, the Met Office is currently developing a new rail surface temperature model, designed to accommodate these future user requirements. This model is centred on the Joint UK Land Environment Simulator (JULES); a community model used as the land-surface component of the Met Office Unified Model (UM), but which can also be used – as we do here – as a stand-alone surface-exchange-scheme driven by forecast output from Numerical Weather Prediction (NWP) models. By adapting JULES to model the energy balance of the rail, we are able to produce forecasts of rail surface temperatures. In particular, by driving JULES with output from the Met Office regional ensemble model MOGREPS-UK, we are able to create a set of possible rail forecast outputs. Considering these in aggregate allow us to produce probabilistic forecasts of rail surface temperatures. Output from the rail surface temperature model has been compared to observation data collected at 40 locations across Northern Ireland. Initial analysis shows the model significantly outperforms traditional forecasting methods based on linear relationships with air temperature. Additionally, producing probabilistic forecasts allows to quantify uncertainty, supporting users in moving towards probabilistic, risk-based forecasting. This has the potential to significantly improve heat-related hazard forecasting across the UK railway network, thus improving the safety and efficiency of the network. 

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