We rely on metallic components every day, from cars and bridges to the solder joints in our electronics. In almost all cases, a step in the manufacture of these components is the solidification of liquid alloy, and it is during solidification that most defects arise. We are all familiar with ice expanding as it solidifies, making ice float on lakes and causing water-filled crevices in rocks and roads to crack open. Most metals do not expand on solidification, but shrink. If this shrinkage is not fed by liquid from elsewhere, a variety of defects can form: the outer surface of the casting can be deformed inwards, pores can grow in the liquid, or cracks can propagate along liquid films between grains, pulling the metal apart. In order to produce metals with fewer defects at a competitive cost, predictive models of defect formation in casting are required. To develop accurate models, we first need a better understanding of the fundamentals of deformation in semi-solid alloys. It has recently been found that solidifying metals share striking similarities to the soils that support our buildings and the partially-molten rock in the earth. In their semi-solid state, metals are made up of numerous crystals (solid particles) surrounded by liquid. Just as is the case of sand grains, these particles have been shown to move around each other when the material as a whole deforms, and the particles rotate and transmit forces between each other. An exciting aspect of this discovery is that the answers to solving metal-casting defects may not lie in the metallurgy section of the library but in the Civil Engineering and Earth Sciences sections. Indeed, models already exist for the deformation of soils and are widely used in Civil Engineering. However, the analogy between metals and soils has only been proven in small-scale experiments carried out to observe the individual particles in semi-solid metals. In the proposed research, we seek to conduct experiments inspired by soil and rock mechanics that will produce results suitable for testing whether the framework at the heart of soil mechanics theory can describe the deformation of semi-solid alloys. We aim to fit semi-solid alloy deformation into an over-arching framework for soils, magmas and metals. We will test scientifically whether semi-solid metals meet rules for behaviour specified within Critical State Soil Mechanics theory, developed in the UK in the 1960s. Three main hypotheses must be demonstrated: 1. That the mechanical behaviour depends on the initial packing-density of the crystals: a densely packed material should experience a reduction in packing-density (dilation) when a shearing deformation is applied. The opposite effect (contraction) should be experienced in a loosely packed material. 2. That the peak shear-stress that the material can resist depends on the overall-pressure acting on it. 3. That there is some combination of crystal shape, packing-density and confining pressure where the material can deform without any overall change in packing-density. To achieve this goal, we will combine experimental approaches from soil, magma and metals research. We will use apparatus developed to study partially-liquid rock (magma) to obtain data on deforming semi-solid aluminium alloys at more than 500C. Next, to ensure the correct microscopic interpretation of the measurements, we will directly observe crystals within a semi-solid alloy as it is being deformed in a small-scale two-dimensional experiment using X-ray imaging in Japan. We will then develop an equivalent particle-scale computer model, based on soil mechanics, of the X-ray experiments to explore the forces acting at crystal-crystal contacts. When combined, the results from the experiments and modelling should enable us to put forward a new idea for the modelling of semi-solid metals.

Organic semiconductors are becoming a very powerful electronic technology for applications in flexible displays and low-cost printed circuits. Their charge transport physics and ultimate performance limits are however not well understood. The objective of the proposed project is to establish an intense collaboration between the Osaka and Cambridge organic electronic groups in order to arrive at an in-depth understanding of the relationship between the device physics of conjugated polymers and molecular crystals. We will perform a broad range of directly comparable experiments on the two systems using techniques that are already available in the Osaka and Cambridge groups to understand similarities and differences in the charge transport physics of the two systems. This will include performing the first Hall effect and magnetoresistance measurements on high-mobility polymer semiconductors to compare with measurements already performed in Osaka on molecular crystals. A particularly interesting question is that of polaronic relaxation processes in molecular crystals, and we will perform the first spectroscopic measurements of charge-induced optical absorptions in molecular crystals and compare with those already performed on polymers in Cambridge. The core of the research work outlined above will be carried out by two PhD students, one registered in Cambridge, the other one registered in Osaka. Both students will interact with each other very closely, and will spend significant time during their PhD working in the other location. The two PhD students working on the project will have available the widest possible spectrum of experimental characterisation techniques, and the project will provide an excellent training environment for them to become leaders in future UK-Japan research collaborations.

Photostimulation is the application of light to living biological cells in order to alter their behaviour by modifying their chemical properties. This can involve applying chemicals to the sample such as caged molecules and then using light to open the cage to invoke a reaction or by instigating a response in chemicals already present within the cells. The most common use of the latter method is in the activation of a light-sensitive protein such as rhodopsin, which can then excite the cell expressing the opsin. Recently, researchers at the Laboratory for Scientific Instrumentation and Engineering have used laser sources to stimulate other biological processes such as calcium waves in live cells. However, the laser systems currently used by researchers at LaSIE for this procedure only permits spatially precise photostimulation in live, dissociated cells and not in thick biological tissue. The development of laser technology to allow three-dimensional control over the photostimulated region deep within thick tissue samples would greatly extend the capability of this technique, with the longer-term potential of in vivo photostimulation at depth. This approach, which would be compatabile with current bio-imaging techniques, would offer a new method to study fundamental properties of cells and their behaviour in a less invasive manner than is currently possible. The overseas visit of Dr Gail McConnell and Mr Elric Esposito is proposed to plan a collaborative research project to develop laser technology dedicated to spatially-localised, deep-tissue photostimulation. This would involve learning more about the practical techniques associated with photostimulation of live cells from researchers at LaSIE and the exploration of collaborative funding opportunities to pursue this project. It is intended that Mr Esposito would perform the project at the Centre for Biophotonics as the appointed post-doctoral research fellow, with collaborative support from Dr Nicholas Smith at LaSIE as the project partner and the host of our intended visit.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

This project lies in the field of euclidean harmonic analysis, and in particular the so-called restriction theory of the Fourier transform. This mathematical theory concerns the manner in which families of waves propagating in different directions in euclidean space can interact, and establishes deep inequalities that estimate this interaction effectively. This area has seen remarkable growth and impact over the last decade, considerably deepening its connections with other branches of mathematics, such as differential equations, combinatorial geometry, algebraic geometry and number theory. This project places particular emphasis on the development of a powerful and widely-applicable new methodology, and its potential to transform Fourier restriction theory. This methodology, naturally termed Tomographic Fourier Analysis, is designed to reveal the extent to which superpositions of waves in space (referred to as Fourier extensions) may be studied effectively via their "sections" or "slices". This simple idea opens a new and direct route by which classical methods of Fourier analysis may be applied to contemporary problems in harmonic analysis. The specific objectives are to establish a range of important conjectural inequalities that control Fourier extensions in terms of classical tomographic transforms, such as the X-ray and Radon transforms (the so-called Mizohata-Takeuchi and Stein conjectures). In particular, establishing such control would profoundly strengthen the longstanding high-profile interface of harmonic analysis with combinatorial geometry, and clarify the mysterious relationship between the celebrated Fourier restriction and Kakeya conjectures. Complex wave-like phenomena of the type described above pervade the mathematical sciences, and are notoriously difficult to understand. The tools developed in the proposed research allow the underlying oscillatory structures (so-called oscillatory integral operators) to be viewed in purely geometric and combinatorial ways. This has the potential for significant applications and benefits in the longer term. Furthermore, the methodology (Tomographic Fourier Analysis), as its name indicates, has the potential to benefit mathematics through novel two-way interactions between the harmonic analysis and inverse problems communities.