Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.Read moreRead less
Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and sp ....Improving transient performance for systems with multiple inputs/outputs. This project aims to develop and test new mathematical techniques for the improvement of transient performance in tracking control systems. The fundamental problem to be addressed will be the design of controllers to rapidly track constant and time varying target reference signals without overshooting or undershooting for multiple-input multiple-output systems/plants. These new methods aim to offer improved accuracy and speed in many engineering applications.Read moreRead less
System identification of microstructure in the brain using magnetic resonance. Magnetic Resonance Imaging technologies will be exploited to probe the microstructure of the brain, using powerful Bayesian optimisation techniques and innovative uses of magnetic resonance. The project will in particular develop non-invasive imaging methods to quantify iron content in the brain, important for research on dementia and Alzheimer's disease.