Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fracti ....A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fractional operators used in modern practice and how to impose boundary conditions on finite domains. Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.Read moreRead less