Applied and Industrial Mathematics

The project investigates piezoelectric wave energy converters used in marine engineering. It involves developing mathematical and computational models for the interaction between complex fluid motion and deformable structures allowing these wave energy systems to be analysed and their effectiveness assessed.

Joint with a team of UTS’s geotechnical engineers, this project studies the fundamental mechanics of railway ballast particles interacting with Rubber Energy Absorbing Grids (REAG) manufactured from recycled rubber. It aims to develop a more robust track design with increased track longevity and reduced maintenance costs.

Joint with a team of UTS’s geotechnical engineers, this project aims to study and quantify the benefits of an energy-absorbing layer of railway ballast containing recycled rubber interacting with sleepers (composed of recycled plastic and glass fibres) to reduce breakage, noise and vibration.

This project is to develop an analytical-numerical model for the propagation of acoustic gravity waves in a coupled atmosphere-ocean system to provide a predictive tool for the magnitude and arrival time of tsunamis from pressure measurements in the ocean or atmosphere.

This multidisciplinary project aims to develop modelling approaches both mathematically and computationally to determine mechanics of nanostructures used in various applications, such as drug delivery, energy storage and nanosensors. This project involves collaboration across chemistry and material science disciplines.

This project involves the application of hydroelasticity to the modelling of complex motion of sea ice and ice shelves as they are influenced by ocean waves. It has application to the breakup and extend of sea ice and the breakup of ice shelves.

This project models simplified ships travelling along a free surface to understand the intrinsic behaviour of ship generated waves. Insights from this project informs the inverse problem of using information about the water’s surface (e.g. height over time) to infer information about the ship that generated the observed waves.

This project analyses wave transmission in and scattering by complex metamaterials. Analysis of the spectral properties of associated highly nonselfadjoint differential operators enables modelling of feedback, delay, and nonlocal control effects.

This project discovers, classifies, and explains dispersive revival, quantization, and fractalization effects in dispersive systems. Novel algorithms for the (approximate) solution of dispersive systems are analysed. Applications include mathematical encryption, optics, and quantum mechanics.

This project is about designing simple and efficient finite element methods for Biot poro-elasticity. Biot poro-elasticity model describes the mechanical behaviour of fluid-saturated porous materials, such as soils, rocks and biological tissues. This is a coupled model that combines the deformation of a porous solid matrix with the flow of fluid in porous medium.

This project considers fourth and sixth order partial differential equations and design constrained minimisation formulations with the aim to develop efficient finite element methods. Then we extend the approach to time-dependent problems.

This project is concerned with designing simple numerical approaches to remove the mixture of Gaussian and impulsive noise from an image. We use different numerical techniques combined with physically informed neural networks to remove the mixture noise. We also consider numerical techniques to smooth a function given by values in scattered data.

This project investigates teaching aspects of undergraduate mathematics courses at the University of Newcastle. It aims to enhance the delivery of our mathematics courses to better engage and connect with our students. Our teaching is also driven by research conducted within our group, reflecting strong research–teaching nexus.