Mimetic and stable numerical methods for nonlinear shallow water equations

The modelling of high dimensional data sets pose a particular challenge both for approximation and the parallel implementation. In this project we investigate the parallelization of sparse grid methods.

The goal of this project is to compute the particle orbits in a MRxMHD equilibrium with fully 3D field and quantify the impact of the islands and chaos to particle confinement.

Develop mathematical models for disease spread that take into account human mobility and population dynamics, which can be calibrated using machine learning methods.

In this project we rederive and implement a recently published quantum algorithm for the Vlasov-Maxwell system of equations in Q#, a quantum computation platform.

Recent development of a flowing MHD model for a rotating, collisional plasma column discovered the intriguing prediction of opposite axial acceleration of the plasma ions in the subsonic and supersonic regimes. This project would examine the regime above, below, and through the shock.

For people involved in the Mathematical Modelling and Computation program, research opportunities exist in formulation of fault-tolerant numerical schemes, implementation of fault-tolerant schemes on supercomputers, simulation of hardware failure events on ultrascale supercomputers, and application of these techniques to scientific computing.

Describe the theoretical properties of methods based on machine learning to solve forward, inverse and operator design problems associated with partial differential equations.

Sensitivity analysis is an important tool in evaluating model behaviour and assessing which parameters are significant, as well as the interactions between parameters.

Shaping value of information to real world conditions in water decision making

I am interested in using a multi-parameter study of invariants from algebraic topology to do statistical shape analysis. The goal is to quantitatively compare geometric objects such as a set of bones, tumours, leaves, bird beaks, etc. I have both theory and application projects.

This project aims to characterise the properties of network-packet captures (both batched and streaming), and use a combination of statistical techniques , Fourier and higher order spectral methods and correlation analysis techniques to develop candidate reduced “forward-models” for the network parameters.

Fusion plasmas can support a wide range of electromagnetic waves, ranging from pressure and current gradient driven modes to those driven unstable by fast particle-wave resonance. The diagnosis and control of fusion plasmas is contingent on the accurate modelling, prediction, and reliable measurement of such modes.

This project seeks to provide a fundamental understanding of the process of energetic particle redistribution from the perspective of thermodynamics and entropy.

Mathematical innovation relating to data science