The achievements of modern research and their rapid progress from theory to application are increasingly underpinned by computation. Computational approaches are often hailed as a new third pillar of science - in addition to empirical and theoretical work. While its breadth makes computation almost as ubiquitous as mathematics as a key tool in science and engineering, it is a much younger discipline and stands to benefit enormously from building increased capacity and increased efforts towards integration, standardization, and professionalism. The development of new ideas and techniques in computing is extremely rapid, the progress enabled by these breakthroughs is enormous, and their impact on society is substantial: modern technologies ranging from the Airbus 380, MRI scans and smartphone CPUs could not have been developed without computer simulation; progress on major scientific questions from climate change to astronomy are driven by the results from computational models; major investment decisions are underwritten by computational modelling. Furthermore, simulation modelling is emerging as a key tool within domains experiencing a data revolution such as biomedicine and finance. This progress has been enabled through the rapid increase of computational power, and was based in the past on an increased rate at which computing instructions in the processor can be carried out. However, this clock rate cannot be increased much further and in recent computational architectures (such as GPU, Intel Phi) additional computational power is now provided through having (of the order of) hundreds of computational cores in the same unit. This opens up potential for new order of magnitude performance improvements but requires additional specialist training in parallel programming and computational methods to be able to tap into and exploit this opportunity. Computational advances are enabled by new hardware, and innovations in algorithms, numerical methods and simulation techniques, and application of best practice in scientific computational modelling. The most effective progress and highest impact can be obtained by combining, linking and simultaneously exploiting step changes in hardware, software, methods and skills. However, good computational science training is scarce, especially at post-graduate level. The Centre for Doctoral Training in Next Generation Computational Modelling will develop 55+ graduate students to address this skills gap. Trained as future leaders in Computational Modelling, they will form the core of a community of computational modellers crossing disciplinary boundaries, constantly working to transfer the latest computational advances to related fields. By tackling cutting-edge research from fields such as Computational Engineering, Advanced Materials, Autonomous Systems and Health, whilst communicating their advances and working together with a world-leading group of academic and industrial computational modellers, the students will be perfectly equipped to drive advanced computing over the coming decades.

Tony Skyrme proposed that under special circumstances it is possible to stabilize vortex-like whirls in fields to produce topologically stable objects. This idea, effectively of creating a new type of fundamental particle, has been realised with the recent discovery of skyrmions in magnetic materials. The confirmation of the existence of skyrmions in chiral magnets and of their self-organization into a skyrmion lattice has made skyrmion physics arguably the hottest topic in magnetism research at the moment. Skyrmions are excitations of matter whose occurrence and collective properties are mysterious, but which hold promise for advancing our basic understanding of matter and also for technological deployment as highly efficient memory elements. Following the discovery of skyrmions in a variety of materials, several urgent questions remain which are holding back the field: what are the general properties of the phase transitions that lead to the skyrmion lattice phase, the nature of its structure, excitations and stability and how might we exploit the unique magnetic properties of this matter in future devices? These questions have only recently begun to be addressed by several large international consortia and are far from being resolved. For the UK to contend in this highly competitive field a major project is required that brings together UK experts in materials synthesis and state-of-the-art theoretical and experimental techniques. We propose the first funded UK national programme to investigate skyrmions, skyrmion lattices and skyrmionic devices. Our systematic approach, combining experts from different fields is aimed at answering basic questions about the status of magnetic skyrmions and working with industrial partners to develop technological applications founded on this physics.