# Scientific interests

My scientific research is in the broad area of complex systems - multi-component systems exhibiting interesting collective properties that cannot be easily understood in terms of the properties of the individual components. To be more specific, my research has three main strands:

## Fluid dynamics, turbulence and nonlinear waves

We are surrounded by fluid dynamics every day of our lives. The air we breath, the water we drink and the blood that constantly circulates inside our bodies are only a few examples. Fluid flows - particularly turbulent flows - are often strikingly beautiful. They exhibit beguiling layers of nested structure and complexity. Yet this beauty is mostly invisible to us. Most fluids are either transparent or opaque so we never see their motion directly. I find this fascinating. Mathematical analysis, computer simulations and experimental measurements can reveal the hidden internal structure of turbulent flows. My research in fluid dynamics is mostly concerned with how organised structures like vortices, jets and waves emerge from and co-exist with random turbulent fluctuations.

## Kinetic theory of systems far from equilibrium

The theory of equilibrium statistical mechanics explains how macroscopic properties of matter like temperature, pressure and magnetisation emerge from the dynamics of incomprehensibly huge numbers of individual atoms. This theory is one of the greatest achievements of physics. Of particular note is its characterisation of the elegant rescaling symmetries observed at phase transitions. These are conditions under which matter undergoes qualitative changes from one equilibrium state to another such as the transition from a liquid to a gas. Many systems of scientific interest are, however, far from equilibrium. The theory of equilibrium statistical mechanics does not apply to them. Kinetic theory is a complementary approach extending statistical mechanics to include a description of the dynamics of systems far from equilibrium. My research in this area is focused on systems whose dynamics is controlled by flows (or currents) of some conserved quantity like energy or mass. Examples include the kinetics of coagulation processes like droplet coagulation inside clouds or the kinetics of waves on the surface of the ocean.

## Industrial mathematics and applications of data science

The history of science tells us that revolutionary discoveries result from scientists following their curiosity. On the other hand, the argument is often made (mostly by non-scientists) that publicly funded research should focus on solving problems that are identifed a-priori as having immediate practical or commercial value to society. In my view, both of these perspectives are correct - the only real question is how to maintain a balance that delivers on both. In this context, although I am a theoretical physicist by nature and interested by theoretical questions, I am also intrigued by the digitisation of the world that has occurred during my lifetime and enjoy exploring how mathematical models and data integrate together to produce new technological capabilities. Examples of my applied research interests include assimilation of sensor data in "fluid dynamical" models of traffic flow and the use of market data to infer financial risk.