Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical un ....Outflows, Jets and Plumes. This project studies how fluid flows out from a small concentrated object into a second surrounding fluid. New solution methods will be provided, and new results about how these fluid flows evolve will be obtained. These are important problems with significance in modelling underwater explosions. They are also important in astrophysics, and will help explain the shapes of outflows from some stars or galaxies. The outcomes of the project will be a deeper mathematical understanding of which outflow shapes are stable, and under what circumstances they might become unstable. This will provide valuable information about galaxy shapes, and a new suite of computational methods for solving such problems.Read moreRead less
Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi- ....Mathematical modelling of the dynamics of multi-layered biological tissues. The project intends to develop a mathematical model of the basic mechanisms that determine the self-organisation of cells into complex tissues during the development of the embryo. Tissue function requires a non-trivial tissue architecture often composed of multiple cell layers which exhibit a remarkable capacity for renewal and defect correction. A cardinal part of embryonic development involves robust shaping of multi-layered tissue morphologies. The project plans to use mathematical models to determine how complex, three-dimensional structures arise from adaptive multicellular biomechanical interactions. It plans to develop a novel computational modelling framework to represent and analyse such systems, which may be applicable to a wide range of problems where tissue mechanics is a key factor such as bone remodelling and wound healing.Read moreRead less
How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has p ....How motor proteins contract the cell cortex and form a cell division ring. This project aims to develop a detailed physical model for motor proteins and filaments and, based on it, derive a fluid-type mean-field mathematical model, which will facilitate numerical simulations and lead to testable predictions. This study will also provide detailed quantitative information on how these processes can be controlled by modifying concentration and properties of structural and motor proteins. This has potential applications in tumour therapy, developmental biology and in the bioengineering of nanomaterials.Read moreRead less
Shining the light on geometry of microstructured optical fibres. A fast, powerful computer code using new mathematical models and techniques will be produced and experimentally validated, for use in development of novel microstructured optical fibres for telecommunications and other applications. This code will reduce the time-consuming and expensive experimental iteration needed for development of these fibres.
Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve th ....Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve the models and experimentally validate solutions. This work will direct future design of microstructured optical fibres to empower next-generation optical-fibre technologies. Expected outcomes are fibre designs for telecommunications, medicine, biotechnology, sensing and imaging.Read moreRead less
Pattern formation of precursor films: a new mathematical model. This project aims to develop a new mathematical model to predict the pattern formation of a new class of permanent lubricants. Ionic liquids are conductive and do not evaporate, creating a unique opportunity to develop such coatings. These thin films form patterns where the pattern type (patches, stripes or holes) depends on the liquid/surface interaction. Only some patterns result in good lubrication; current limited understanding ....Pattern formation of precursor films: a new mathematical model. This project aims to develop a new mathematical model to predict the pattern formation of a new class of permanent lubricants. Ionic liquids are conductive and do not evaporate, creating a unique opportunity to develop such coatings. These thin films form patterns where the pattern type (patches, stripes or holes) depends on the liquid/surface interaction. Only some patterns result in good lubrication; current limited understanding of the pattern formation process hampers selection of a good lubricant for a chosen material. Current mathematical approaches are computationally expensive and time consuming. The new model expected from this project would provide a cheap, fast and reliable alternative for screening suitable liquid/surface pairs.Read moreRead less
Seismology of solar and stellar magnetic activity. Seismic techniques for looking inside stars using observations of surface oscillations can be confused by the very surface magnetic fields that produce flares and other activity and that we wish to probe. This project will develop a new ray-based code, SunRay, which will be able to explore active regions taking full account of magnetic effects.
Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the interna ....Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the internal detail of micro-structured materials. Recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project aims to investigate how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.Read moreRead less
Dynamics of fire whirls and dust devils. The project aims to develop fundamental understanding and models to inform the development of more accurate computer models of fire front propagation. Fire whirls and dust devils are strongly swirling localised vortex flows that result from an interplay of circulation and buoyancy, may extend hundreds of metres into the air. By projecting firebrands well away from the ground strike, fire whirls can initiate spot fires well beyond a fire front, advancing f ....Dynamics of fire whirls and dust devils. The project aims to develop fundamental understanding and models to inform the development of more accurate computer models of fire front propagation. Fire whirls and dust devils are strongly swirling localised vortex flows that result from an interplay of circulation and buoyancy, may extend hundreds of metres into the air. By projecting firebrands well away from the ground strike, fire whirls can initiate spot fires well beyond a fire front, advancing fronts at much higher speeds than most fire spread models predict. The project aims to improve understanding of the sets of local conditions that produce and stabilise these flows, using computational fluid dynamics matched to laboratory experiments and dimensional analysis of results.Read moreRead less