This proposal aims to investigate a range of perovskite structured thin films using a combination of Raman spectroscopy, in-situ transmission electron microscopy and synchrotron X-radiation in order to determine how constraint controls the onset and temperature dependence of octahedral tilt transitions in thin films and ensuing domain structure. It is anticpated that this will give a greater understanding of how constraint influences functional properties in ferroelectric and dielectric thin layers. The proposal will concentrate on three key systems in which tilt transitions are known to influence macroscopic properties; PbZrxTi(1-x)O3, Ag(Nb,Ta)O3 and the newly discovered (1-x)BiMeO3-xPbTiO3 solid solutions. The proposal is joint between University of Sheffield, Pennsylvania State University and Argonne National Laboratory. The latter will submit an independent National Science Foundation proposal which directly compliments the work proposed here. The programme is for 4 years at the request of the National Science Foundation, USA.

Optical fibres form the physical layer of the remarkable >2 billion km long global telecommunications network, currently bifurcating and expanding at a rate >Mach 20, i.e. over 14000 ft/sec (source: Corning.com). They are also an essential component in devices such as lasers, optical amplifiers, gyroscopes, gas or environmental sensors, as well as a means to locally link devices and applications. One of the most significant advances in optical fibre technology over the last 20 years has been the realisation of silica fibres that are able to internally guide light using an air core rather than glass. Hollow Core Photonic Bandgap Fibres (HC-PBGFs) were first demonstrated in the late 1990s. Researchers uncovered remarkable physics, demonstrating that these fibres were able to transmit high optical powers, ultrashort pulses and wavelengths regions including the mid-IR which cannot be delivered through standard optical fibres. A number of important applications can be targeted within these wavelength regions and in particular mid-infrared light can be used to detect a wide range of chemical, biological or physical species (e.g. to identify explosives on surfaces, hazardous air pollutants in the environment, or biomarkers in the breath of a patient). The last few years have seen dramatic progress in the area of hollow fibres and in particular the development of a competing technology to photonic bandgap fibres based on a much simpler optical design, which are far easier to fabricate for both short and long wavelength transmission and have been demonstrated to have a greatly reduced overlap between the light travelling within the fibre and the silica forming the cladding. This novel form of hollow core optical waveguide is known as the anti-resonant fibre. In this proposal, we will demonstrate an innovative waveguide platform based on composite material hollow core fibres which are able not only to transmit optical signals with low attenuation over a broad wavelength range of operation, but can also actively manage and control the transmitted signals, through modulation, amplification or light generation and frequency conversion.

The Innovative Manufacturing and Construction Research Centre (IMCRC) will undertake a wide variety of work in the Manufacturing, Construction and product design areas. The work will be contained within 5 programmes:1. Transforming Organisations / Providing individuals, organisations, sectors and regions with the dynamic and innovative capability to thrive in a complex and uncertain future2. High Value Assets / Delivering tools, techniques and designs to maximise the through-life value of high capital cost, long life physical assets3. Healthy & Secure Future / Meeting the growing need for products & environments that promote health, safety and security4. Next Generation Technologies / The future materials, processes, production and information systems to deliver products to the customer5. Customised Products / The design and optimisation techniques to deliver customer specific products.Academics within the Loughborough IMCRC have an internationally leading track record in these areas and a history of strong collaborations to gear IMCRC capabilities with the complementary strengths of external groups.Innovative activities are increasingly distributed across the value chain. The impressive scope of the IMCRC helps us mirror this industrial reality, and enhances knowledge transfer. This advantage of the size and diversity of activities within the IMCRC compared with other smaller UK centres gives the Loughborough IMCRC a leading role in this technology and value chain integration area. Loughborough IMCRC as by far the biggest IMRC (in terms of number of academics, researchers and in funding) can take a more holistic approach and has the skills to generate, identify and integrate expertise from elsewhere as required. Therefore, a large proportion of the Centre funding (approximately 50%) will be allocated to Integration projects or Grand Challenges that cover a spectrum of expertise.The Centre covers a wide range of activities from Concept to Creation.The activities of the Centre will take place in collaboration with the world's best researchers in the UK and abroad. The academics within the Centre will be organised into 3 Research Units so that they can be co-ordinated effectively and can cooperate on Programmes.

Nonlinear partial differential equations (NPDEs) are at the heart of many scientific advances, with both length scales ranging from sub-atomic to astronomical and timescales ranging from picoseconds to millennia. Stability analysis is crucial in all aspects of NPDEs and their applications in Science and Engineering, but has grand challenges. For instance, when a planar shock hits a wedge head on, a self-similar reflected shock moves outward as the original shock moves forward in time. The complexity of shock reflection-diffraction configurations was reported by Ernst Mach in 1878, and later experimental, computational, and asymptotic analysis has shown that various patterns of reflected-diffracted shocks may occur. Most fundamental issues for shock reflection-diffraction have not been understood. The global existence and stability of shock reflection-diffraction solutions in the framework of the compressible Euler system and the potential flow equation, widely used in Aerodynamics, will be a definite mathematical answer. Another example arises in the analysis of mean field limits, a powerful tool in applied analysis introduced to bridge microscopic and macroscopic descriptions of many body systems. They typically involve a huge number of individuals (particles), such as gas molecules in the upper atmosphere, from which we want to extract macroscopic information. Multi-agent systems have become more popular than ever. In addition to their new classical applications in Physics, they are widely used in Biology, Economy, Finance, and even Social Sciences. One key question is how this complexity is reduced by quantifying the stability of the mean field limit and/or their hydrodynamic approximations. By forming a distinctive joint force of the UK/US expertise, the proposed research is to tackle the most difficult and longstanding stability problems for NPDEs across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic systems of conservation laws, kinetic equations, and related multiscale applications in transonic/viscous-inviscid/fluid-particle models. Through this rare combination of skills and methodology across the Atlantic, the project focuses on four interrelated objectives, each connected either with challenging open problems or with newly emerging fundamental problems involving stability/instability: Objective 1. Stability analysis of shock wave patterns of reflections/diffraction with focus on the shock reflection-diffraction problem in gas dynamics, one of the most fundamental multi-dimensional (M-D) shock wave problems; Objective 2. Stability analysis of vortex sheets, contact discontinuities, and other characteristic discontinuities for M-D hyperbolic systems of conservation laws, especially including the equations of M-D nonisentropic thermoelasticity in the Eulerian coordinates, governing the evolution of thermoelastic nonconductors of heat; Objective 3. Stability analysis of particle to continuum limits including the quantifying asymptotic/mean-field/large-time limits for pairwise interactions and particle limits for general interactions among multi-agent systems; Objective 4. Stability analysis of asymptotic limits with emphasis on the vanishing viscosity limit of solutions from M-D compressible viscous to inviscid flows with large initial data. These objectives are demanding, since the problems involved are of mixed-type and multiscale, as well as M-D, nonlocal, and less regular, making the mathematical analysis a formidable task. While many of the problems in the project have been known for some time, it is only recently that their solutions seem to have come within reach; in fact, part of the project would have been inconceivable prior to 2010. The simultaneous study of problems associated with the four objectives above will lead to a more systematic stability analysis for NPDEs across multiscale applications.

For a wide range of applied (pest control, disease outbreak, harvesting strategies) and fundamental reasons (climate change) ecologists need to understand not only what determines the abundance of a species but also how abundance varies over time and why these patterns differ from one location to another. Considerable effort has been devoted to exploring this issue, especially in species with unstable dynamics but in only a few instances do we now have the insight into the major mechanisms. These studies have tended to focus attention on the role of single biotic factors, such as predation or parasitism, and some studies have also considered the interaction between a biotic process and climate. Yet we know that populations are governed by a variety of biotic processes and that these commonly interact. So, a major challenge, and the overall aim of this proposal, is to quantify the impact of interactions between biotic factors in relation to their climatic context on population dynamics. We will work on the red grouse, a species in the British uplands whose populations commonly show cyclic dynamics. There is considerable variation in grouse population dynamics between areas, with some populations not cyclic, and the cycle period of the strongly cyclic populations varying from 4 to 12 years. This study system and the variation within it provides us with an excellent opportunity to quantify the impact of interactions between biotic processes. Grouse have been well studied, so we can identify and manipulate the two dominant biotic processes: parasitism and territorial behaviour. Moreover, we also know that territorial behaviour and parasite intensity affect each other. However, we do not know how abiotic factors affect these interactions and how the interactions in turn affect individual fitness and emergent dynamics. Our specific aim is to test the hypothesis that the spatial variation we observe in the cyclic dynamics of grouse is the result of parasites and territorial behaviour interacting within a gradient of rainfall. To achieve this aim we have built on a successful team of empiricists by collaborating with two theoreticians, skilled in dynamic game theory and population modelling. With this team we will test our hypothesis through experimentation, modelling and testing predictions on long-term time series. We will conduct two experiments that will tell us a) how parasite intensity varies with territorial behaviour and vice-versa, b) how these interactions influence breeding success and survival across an environmental gradient; and c) what the transmission rate is between male and female grouse within pairs. A quantification of transmission between sexes is necessary to combine previous models and data. Given that more aggressive grouse pickup more parasites, we will use game theory to explore the implications of this interaction for how much individual males should invest in territorial behaviour. With input from the experiments and game theory, the population dynamic consequences of the strategy decisions will be investigated through population models. For grouse populations in locations with given values of rainfall the population models will predict what cyclic patterns would be expected. We will the test these predictions against the long-term time series of harvest records available from managed grouse moorlands across the country. Our findings will highlight the role played by interactions between biotic factors on population dynamics. This is an important issue, as it will help us understand how climate change and management will interact to influence abundance and dynamics. In Britain, these studies are both timely with respect to our current knowledge and the dramatic ecological changes being observed in parts of the uplands.