I work on the development, analysis and application of mathematical and computational methods to real-world systems, with a focus on problems which require modelling over different spatial and temporal scales. Mathematical approaches include differential equations (PDEs, ODEs), stochastic processes, numerical analysis, Monte Carlo simulations and molecular dynamics algorithms.
Applications often come from biology where I am interested in understanding the behaviour of complex systems consisting of many interacting components. An example is modelling interactions between individual genes and proteins inside a cell which lead to a specific behaviour of the whole cell. These models can be formulated in terms of the behaviour of individual macromolecules which is simulated on a computer. Molecular-based simulations are popular because they can incorporate known molecular biology and can be used to find how changes at the molecular-level lead to desired changes (e.g. treatment) of cell-level properties.
However, it is often challenging to efficiently simulate large collections of macromolecules over system-level time scales. I am working on developing algorithms which enable this.
For example, in some applications, microscopic detail is only required in a relatively small region (e.g. close to a cell membrane or a particular organelle). One way to achieve this detail is to use a computationally intensive model over the whole simulation domain (cell). A better way is to develop and implement algorithms which can efficiently and accurately couple molecular-based models with less detailed computationally efficient descriptions.
These multiscale (hybrid) approaches use a detailed modelling approach in localized regions of particular interest (in which accuracy and microscopic detail is important) and a less detailed model in other regions in which accuracy may be traded for simulation efficiency.