The proposed EPSRC CDT in the Science and Applications of Graphene and Related Nanomaterials will respond to the UK need to train specialists with the skills to manipulate new strictly two-dimensional (2D) materials, in particular graphene, and work effectively across the necessary interdisciplinary boundaries. Graphene has been dubbed a miracle material due to the unique combination of superior electronic, mechanical, optical, chemical and biocompatible properties suitable for a large number of realistic applications. The potential of other 2D materials (e.g. boron nitride, transition metal and gallium dichalcogenides) has become clear more recently and already led to developing 'materials on demand'. The proposed CDT will build on the world-leading research in graphene and other 2D nanomaterials at the Universities of Manchester (UoM) and Lancaster (LU). In the last few years this research has undergone huge expansion from fundamental physics into chemistry, materials science, characterization, engineering, and life sciences. The importance of developing graphene-based technology has been recognized by recent large-scale investments from UK and European governments, including the establishment of the National Graphene Institute (NGI) at UoM and the award of 'Graphene Flagship' funding by the European Commission within the framework of the Future and Emerging Technologies (Euro1 billion over the next 10 years), aiming to support UK and European industries.Tailored training of young researchers in these areas has now become urgent as numerous companies and spin-offs specializing in electronics, energy storage, composites, sensors, displays, packaging and separation techniques have joined the race and are investing heavily in development of graphene-based technologies. Given these developments, it is of national importance that we establish a CDT that will train the next generation of scientists and engineers who will able to realise the huge potential of graphene and related 2D materials, driving innovation in the UK, Europe and beyond. The CDT will work with industrial partners to translate the results of academic research into real-world applications in the framework of the NGI and support the highly successful research base at UoM and LU. The new CDT will build directly on the structures and training framework developed for the highly successful North-West Nanoscience DTC (NOWNANO). The central achievement of NOWNANO has been creating a wide ranging interdisciplinary PhD programme, educating a new type of specialist capable of thinking and working across traditional discipline boundaries. The close involvement of the medical/life sciences with the physical sciences was another prominent and successful feature of NOWNANO and one we will continue in the new CDT. In addition to interdisciplinarity, an important feature of the new CDT will be the engagement with a broad network of users in industry and society, nationally and internationally. The students will start their 4-year PhD with a rigorous, bespoke 6-month programme of taught and assessed courses covering a broad range of nanoscience and nanotechnology, extending beyond graphene to other nanomaterials and their applications. This will be followed by challenging, interdisciplinary research projects and a programme of CDT-wide events (annual conferences, regular seminars, training in transferable skills, commercialization training, outreach activities). International experience will be provided by visiting academics and secondments to overseas partners. Training in knowledge transfer will be a prominent feature of the proposed programme, including a bespoke course 'Innovation and Commercialisation of Research' to which our many industrial partners will contribute, and industrial experience in the form of 3 to 6 months secondments that each CDT student will undertake in the course of their PhD.

This is an extension of the Fellowship: 'NEMESIS' (New Mathematics for Materials Modelling in the Engineering Sciences and Industrial Sectors). Advanced materials sit at the heart of modern technology and are at the forefront of many improvements in quality of life. Key to enhancing material properties is a deep understanding of the link from microstructure to macroscale properties. This requires a diverse range of science including theoretical modelling, computational simulation and experimentation. This Fellowship Extension project sits at the triple point of these approaches and principally, uses the experience of the team, in particular in advanced mathematical modelling in order to design new materials for a range of applications. Three themes will be considered, "Reinforced syntactic foams", "Acoustic metamaterials" and "Thermal metamaterials" and a programme of Public Engagement will illustrate the research to a wide audience. Syntactic foams offer stiff, lightweight materials with strong recoverability, even after significant loading. This theme will investigate the ability of reinforcements including families of 2D materials and other micro and nano fillers in order to enhance stiffness whilst maintaining weight and recoverability. Iteration between models and experiments will ensure that optimise properties are determined. Applications are in marine structures, although a very well-publicised use of syntactic foams was in the football used in the 2006 world cup! Acoustic metamaterials are providing us with new way to manipulate sound. This theme builds on the recent work of the principal investigator's team where, together with an industrial partner he developed and subsequently built microstructured materials that were able to simultaneously slow down sound and also ensure that sound could penetrate the structure. This is a highly non-trivial task and the realisation of such a medium means that it can now potentially be employed in applications where it is important to manipulate sound. Classical examples are in sound attenuation devices, which using this approach could be made more compact. This theme will therefore look to better the designs using more complex microstructures and utilise the medium in more complex geometries. Thermal metamaterials are new media that look to manipulate heat flow and temperature fields. Research so been to direct thermal fields so that regions of space fare protected from high temperatures. In many applications associated with thermal efficiency, it is important to ensure uniform temperature distributions in electronic devices or regions of space within those devices. This is difficult to achieve in complex geometries. This project will look to design and realise new thermal metamaterials whose aim is to be deployed in specific complex geometries in order to ensure thermal uniformity and therefore enhanced heat dissipation and thus improved energy efficiency. The public engagement theme will use results from the original Fellowship of the PI, together with new results from the Extension in order to devise a programme of public engagement with the specific remit of widening participation in Mathematics, Science and Engineering. This will be achieved by devising talks and events aimed at School children, using stands and exhibitions at Science fairs, national competitions and web and social media presence in order to reach out to as broad a community as possible. This inter-disciplinary project is ideal for this in the sense that it sits many academic fields, with its core in Applied Mathematics but employing ideas from Materials Science, Chemistry, Engineering and Physics in order to achieve its goals.

The overall aim of this new CDT is to generate a body of highly-trained, doctoral scientists and engineers expert in the emerging and economically important area of metamaterials and possessing the skills, knowledge and professional attributes required to meet the challenges of employment in industry, academia and other commercial or governmental spheres. We will provide students with a detailed understanding of metamaterials from fundamental theory right through to prototype device design. At the same time they will be formally trained in the wider professional and personal skills such as innovation, engagement, commercial awareness and, importantly, leadership. Metamaterials are widely recognized as one of the most significant recent technical discoveries, highlighted as a top-ten insight of the last decade by Science Magazine. They are also set to become a major economic factor. In 2011 the global market for metamaterials was worth $256M, and is predicted by BCC Research to grow to $760M million by 2016, and to reach almost $2 billion by 2021. While products based on metamaterials are appearing (e.g. metamaterial antennas in mobile handsets and spacecraft; heat-assisted magnetic recording; transparent conductors for displays; surface bound data transfer and noise barriers etc.), the UK must ensure that future developments in these areas are strongly underpinned at the fundamental research level and also supported by highly skilled practitioners. The Government report on "Technology and Innovations Futures: UK Growth opportunities for the 2020s" (2010) lists 'metamaterials' and 'carbon nanotubes and graphene' as two key advanced materials areas. The UK's Ministry Of Defence (MOD) regards metamaterials as a key emerging technology, specifically listing advanced optical materials, advanced materials, bio-inspired technologies, and micro and nano technologies, as key areas, all topics that are of direct relevance to this CDT proposal. We note the comment from Professor Young's (Dstl) letter of support: "Dstl fully supports your proposal as a timely and unique vehicle for training future scientists, engineers and leaders for the benefit of the wider UK defence and security sector." Our cohort-based training will also help fulfil one of Minister David Willets' key aims "To create a more educated workforce that is the most flexible in Europe." To meet this last aim and to stimulate future UK work in this fast moving materials area we will establish a new CDT in a broad range of metamaterials research with PhD training that has an embedded engagement with industry. We will, together with our collaborators from industry, governmental laboratories and universities overseas, strengthen the synergy between physicists and material engineers, building on our pre-existing excellence in metamaterials and functional materials research. The research focus will be on EPSRC's Physical Sciences theme, specifically the sub topics "Photonic Materials, Metamaterials" (one of only three "Growth" research areas for this theme), and "Plasmonics" (a "Maintain" area). In addition, our CDT is relevant to the EPSRC's grand challenges of "Nanoscale Design of Functional Materials", and "Quantum Physics for New Quantum Technologies". There is also significant overlap with the EPSRC ICT "Growth" research areas of "RF and microwave communications" and "RF and microwave devices", which also encompass THz devices. Our team of 33 academics are addressing key and topical challenges across a range of internationally competitive metamaterials research: from microwave metasurfaces to carbon nanotubes, from graphene plasmonics to spintronics, magnonics and magnetic composites, from terahertz photonics to biomimetics. With the recent recruitment of two world leading theoreticians in transformation optics plus new work in acoustics, we shall combine depth and breadth of metamaterial research linked to industrial and Government laboratory researchers

The range of surgical tools for interventional procedures that dissect or fragment tissue has not changed significantly for millennia. There is huge potential for ultrasonic devices to enable new minimal access surgeries, offering higher precision, much lower force, better preservation of delicate structures, low thermal damage and, importantly, enabling more procedures to be carried out on an out-patient or day surgery basis. To realise this potential, and deliver our vision of ultrasonics being the technology of choice for minimal access interventional surgery, a completely new approach to device design is required, to achieve miniaturisation and to incorporate both a cutting and healing capability in the devices. By integrating with innovative flexible, tentacle-like surgical robots, we will bring ultrasonic devices deep into the human body, along tortuous pathways to the surgical site, to deliver unparalleled precision. Unsurpassed precision in challenging neurological, skull-base and spinal procedures as well as in general surgery is attainable through tailoring the robotic-ultrasonic devices to deliver the exact ultrasonic energy to the exact locations required to optimise the surgery. We will achieve this by quantifying the effects of the ultrasonic excitations typical of surgical devices in tissues, at and surrounding the site of surgery, in terms of precision cutting, tissue damage (mechanical damage, thermal necrosis, cavitation) but also the potential to aid regeneration. We will make world-leading advances in ultra-high speed imaging measurements and biophysical analysis, complementing advances in histology and clinical assessment, to develop a combined approach to the characterisation of both damage and regeneration of tissue. Through this holistic approach to device design, we will create integrated robotic-ultrasonic surgical devices tailored for optimised surgery.

For millennia, mankind has recognized the importance of inhomogeneous media: a combination of two or more individual materials. Such materials are far better than the sum of their parts, e.g. leading to a huge increase in stiffness or strength. Today a plethora of so-called composite or smart materials exist enabling wondrous scientific and engineering advances in a many sectors including aerospace, automobile, structural, communications and acoustic engineering, biotechnology and health, leisure and the nuclear sector to name but a few. Inhomogeneous materials also arise naturally in a number of contexts, e.g. biological tissues where there are often several scales of inhomogeneity. A natural, often difficult research challenge is to predict the effective behaviour of inhomogeneous materials from knowledge of the properties of the constituent phases and their distribution. Such materials often possess rather surprising and counter-intuitive properties, for example the speed of sound in bubbly water is faster than that in either water or air! Amongst other benefits, models of inhomogeneous media are important for design optimization strategies for composites, for the replacement of prohibitively costly experiments in engineering applications and for understanding structure-function relationships in biomechanics. In addition to their effective behaviour, the way that waves propagate through such materials is of great importance. In recent times metamaterials have been devised which allow incredible non-intuitive properties such as strong absorption and filtering properties, waveguiding and localization capabilities and the exciting notions of negative refraction, focussing behaviour and even cloaking! This project focuses on the development and application of new mathematical methods and models associated with complex inhomogeneous, generally nonlinear, materials. Three themes focus on (A) Industrial composites, (B) metamaterials and phononics, (C) Soft biomaterials. Despite there being three distinct themes, there exists a great deal of overlap between these topics meaning that methods developed in one area can also apply to other, apparently unconnected topics. This is the beauty of applied mathematics! In theme (A) the team will work with project partner Thales Underwater Systems Ltd in order to understand the way that sound propagates through complex composite materials when they are subject to high pressures. The load significantly modifies the microstructure of the material and subsequent response to propagating waves and as such the prediction of the reflected and transmitted sound field from such materials is a non-trivial task. Theme (B) will further research into hyperelastic cloaking theory, a technique recently developed by the PI, which uses pre-stressed materials in order to guide waves around specific regions of space. They will also understand further the way that special materials with periodic microstructure can act as wave filters by permitting or restricting wave propagation at given frequencies. In particular the interest is tunable materials so that we can modify the material response at will be applying a pre-stress, or magnetic field for example. In theme (C) the team will develop models for the behaviour of soft tissues: tendon and skin, using information from the microstructure in order to ``upscale'' to macroscopic models. Soft tissues are highly deformable and in particular are viscoelastic meaning that energy is lost during deformation. The prediction of the loading and unloading of such materials is a notoriously difficult task, made even harder in skin due to its complex structural organization. A full understanding of the way that such materials behave has a multitude of applications in medicine and pharmaceutical industries. Models developed are continuously informed and iterated by input from experimental collaborators, whose work is of great importance to this project.