X-ray Computed Tomography (XCT) is a scanning technique that enables full 3D visualisation and interrogation of internal and external geometries. It has become popular within industry (particularly manufacturing) and academic research as it enables us to see more than ever before at a variety of length scales and is completely non-destructive. The time taken to obtain this wealth of data is prohibitive to a number of applications with a single scan taking tens of minutes, up to a few hours. The equipment outlined in this proposal will enable high-resolution scans in tens of seconds, and even faster with some fundamental research. This is a UK first that will generate a wealth of scientific advancement. There have been a small countable number of "dynamic" experiments using lab based XCT scanners where a sample such as a novel material is sequentially loaded (e.g. compression) and scanned at each loading step. Here one can observe the changes in the material through time, identifying failure mechanisms, highlighting potential manufacturing improvements and aids in determining material properties. The reason for so few studies is that the number of scans required can lead to acquisition time of days. The substantial gain in speed with this equipment will reduce the total scan time to a matter of minutes with a continuously acquired dataset. The sample can then be evaluated at discrete points in time, and concentrate around the critical onset of failure observed. Scientific advancement in the development of new polymers, ceramics and metal alloys will be considerably accelerated with this unique characterisation capability. Manufacturing applications are often limited to a few high-value components because of the time taken to scan. The significant step change in speed will allow for high-throughput scanning that is desirable within the manufacturing line. This is the first step in a major revolution that will require big data analytics powered by machine learning algorithms to deliver accept/reject decisions in a reasonable time scale. Together this will be a driver for change in achieving 100% inspection of large component batches, at high resolution and at relevant cycle times.

MathSys addresses two of EPSRC's CDT priority areas in Mathematical Sciences: "Mathematics of Highly Connected Real-World Systems" and "New Mathematics in Biology and Medicine". We will train the next generation of skilled applied mathematical researchers to use and develop cutting-edge techniques enabling them to address a range of challenges faced by science, industry and modern society. Our Centre for Doctoral Training will build on the experience and successes of the Complexity Science DTC at Warwick, while refining the scope of problems addressed. It will provide a supportive and stimulating environment for the students in which the common mathematical challenges underpinning problems from a variety of disciplines can be tackled. The need for mathematically skilled researchers, trained in an interdisciplinary environment, has never been greater and is viewed as a major barrier in both industry and government. This is supported by quotes from reports and business leaders: "Systems research needs more potential future leaders, both in academia and industry" (EPSRC workshop on Systems science towards Engineering, Feb 2011); Andrew Haldane (Bank of England, 2012) said "The financial crisis has taught us the importance of modelling and regulating finance as a complex, adaptive system. That will require skills currently rare or missing in the regulatory community - including, importantly, in the area of complexity science"; Paul Matthews (GlaxoSmithKline) stated "Scientists trained in statistical and computational approaches who have a sophisticated understanding of biologically relevant models are in short supply. They will be major contributors in the task of translating insights on human biology and disease into treatments and cures." Our CDT will address this need by training PhD students in the development and innovation of mathematics in the context of real-world systems and will operate in close collaboration with stakeholders from outside academia who will provide motivating problems and real-world experience. Common mathematical themes will include statistical behaviour of complex systems, tipping points, novel methods in control and resilience, hierarchical aggregation methods, model selection and sufficiency, implications of network structure, response to aperiodic forcing and shocks, and methods for handling complex data. Applications will be driven by local and external partner expertise in Epidemiology, Systems Biology, Crop Science, Healthcare, Operational Research, Systems Engineering, Network Science, Financial Regulation, Data Analysis and Social Behaviour. We believe that the merging of real-world applications with development of novel mathematics will have great synergy; applications will motivate and drive mathematical advances while novel mathematics will allow students to solve challenging real-world problems. The doctoral training programme will follow a 1+3 year MSc+PhD model that has proved successful in the Complexity Science DTC. The first year will consist of six months of taught training, followed by 3-month group research projects on problems set by external partners and a 3-month individual research project, leading to an MSc qualification. This preparation will enable the students to make rapid progress tackling their 3-year PhD research project, under the guidance of one mathematical and one application-oriented supervisor, alongside general skills training and group research projects. We have over 50 suitable supervisors with relevant mathematical expertise, all enthusiastic to contribute; they will be supported by a similar number of application-oriented supervisors from across campus and from external partners. The CDT seeks the equivalent of 7 full studentships per year from EPSRC and has commitment from non-RCUK sources for the equivalent of 3 full studentships per year.