I'm a London-based data engineering consultant, currently working for Gutteridge, Haskins & Davey (GHD) to improve the UK's national infrastructure. I'm passionate about exploring the frontiers of mathematics, modelling, and simulation, and proud of my history tackling difficult challenges in science and engineering.
During my undergraduate studies at the Australian National University I enjoyed undertaking research projects, first as part of a Summer Scholarshp programme with the Mathematical Sciences Institute and following that for my Engineering Honours year.
Models are routinely used to predict the flows of water within a catchment given rainfall data. Uses include managing land-use in agriculture, and reducing risks from flooding events. These models are typically calibrated from historical datasets that include rainfall measured throughout the catchment, and runoff in any nearby streams. However, this data takes large amounts of time and resources to collect.
To apply models to catchments that lack this data, we can use regionalisation. This relies on measuring other physical attributes of catchments, such as their topology and foliage cover. Such attributes are typically easier to source than rainfall-runoff data, especially as they vary little with time. An uncalibrated catchment can then use the parameters of calibrated catchments provided they share its physical attributes.
Ultrasound plays an important role in medicine, with uses including imaging, drug delivery, and cancer therapy. This last application works by focussing high-power ultrasound waves onto a tumour, causing highly localised heating. Simulations are used to ensure that the sound waves focus as intended, and to determine the appropriate level of power that is applied. However, the high frequencies involved can make simulation prohibitively computationally expensive.
One way of mitigating these expenses is to exploit symmetry. Often, the ultrasound transducers are shaped like spherical bowls. The sound waves then have the same symmetry, and this can be exploited in the simulation, reducing a three-dimensional problem down to two-dimensions. To do so, discrete sine and cosine transforms are used. These represent the acoustic field in a using functions with certain symmetry properties.This brings computational costs down dramatically.