Mathematics to underpin and drive novel inertial microfluidic technologies. Particles suspended in flow through microfluidic ducts migrate under inertial and drag forcing to different regions in the cross-section depending on particle size, duct geometry and control parameters, enabling isolation of, for example, cancer cells/microplastics from a blood/water sample. Device design needs mathematical models yielding understanding of the particle dynamics, and tools for determining geometry and con ....Mathematics to underpin and drive novel inertial microfluidic technologies. Particles suspended in flow through microfluidic ducts migrate under inertial and drag forcing to different regions in the cross-section depending on particle size, duct geometry and control parameters, enabling isolation of, for example, cancer cells/microplastics from a blood/water sample. Device design needs mathematical models yielding understanding of the particle dynamics, and tools for determining geometry and control parameters. Particle boundary conditions strongly influence the inertial lift and drag forces that drive particle motion. This project will develop these mathematical tools for boundary conditions applicable to both passive and active particles, so driving development of novel devices for existing and new applications.Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
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Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when comple .... Mathematical and Numerical Models of Piezoelectric Wave Energy Converters. The project will investigate piezoelectric wave energy converters. We will derive the equations of motion in a form suitable for use in marine engineering paradigms using variational methods and then solve these analytically and with smoothed particle hydrodynamics. Using these innovative techniques, this project will generate new knowledge capable of elucidating the multifaceted physical phenomena that occur when complex fluid motion and deformable structures interact. The project outcomes include the development of mathematical and computation methods to handle intricate behaviours of piezoelectric elastic-fluids systems. These groundbreaking methods will allow these wave energy systems to be analysed and their effectiveness assessed.Read moreRead less