An Introduction to Dr Donald Brown, his research ..........and haggis!

By Dr Donald Brown, Assistant Professor in Applied Mathematics

That's me!
I would first like to introduce myself; I am a newly appointed Assistant Professor of Applied Mathematics in the School of Mathematical Sciences, having started in September 2015. I am also in the new GeoEnergy Research Centre (GERC), a joint venture between the British Geological Society (BGS) and the University of Nottingham.  I work with the scientific computing group, but also have close overlap in areas of industrial and applied mathematics. Broadly speaking, I work in the area of modelling and numerical analysis on problems arising in porous media with an emphasis in the geosciences.

Before arriving in Nottingham, (many years before) I was born in Cincinnati, Ohio, USA. As Ohio is one of the smaller states I often tell people it is near all the lakes in the middle that looks like a heart.  We also grow a lot of corn and call soda "pop". Fast forward a few years and I completed my PhD in Applied Mathematics at Texas A&M University, USA in 2012. Then, I embarked on a bit of a world tour and went as a postdoctoral research fellow at the Center for Numerical Porous Media, King Abdullah University of Science and Technology, Saudi Arabia from 2012-2014. During this time, I was able to circle the globe so now I have the mathematical distinction of having a "winding-number" of one.

Then, I moved to Europe where I was awarded the Hausdorff Postdoctoral Fellowship, at the University of Bonn, Germany, and from 2014-2015 worked in the Institute for Numerical Simulation in Bonn. Finally, completing (so far) my world tour and was kindly offered an exciting interdisciplinary position to pursue and direct research in the mathematics of GeoEnergy at the University of Nottingham.

My research focus is on multiscale modelling and simulation of subsurface porous media and developing applicable mathematical tools and techniques. The research has wide ranging applications in the modelling of subsurface flows for oil and gas and hydrological applications, as well as what could be called "cross-cutting" areas such as lithium-ion batteries and filtration. Many porous media processes have significant multiscale and multi-physical characteristics. This multiscale nature of porous media often makes solving the full problem intractable and alternative techniques must be employed to bridge these scales. My research is to develop computational tools and analysis techniques to deal with fundamental problems in multiscale processes of subsurface physics.

As someone from a much more sparse country, the first thing I noticed is that the UK has a large and dense network of academics and universities. This makes travelling and attending meetings much faster and easier. One such network is the newly founded UK InterPore Chapter a subset of the porous media society known as InterPore. InterPore is an international society that studies the modelling, simulation, and experimental aspects of porous media in a broadly defined setting. The main theme or idea is that there is an interplay between the tools and techniques across a range of porous media applications from subsurface modelling, industrial, and biological porous media and that these cross-cutting techniques can be discovered, discussed and developed at InterPore meetings.  I recently attended a UK InterPore meeting in Edinburgh, Scotland this January at the International Centre for Mathematical Sciences.
The Haggis (left) - tasty and nothing to be afraid of!

It was not the first time I have been to Edinburgh, but it is the first occasion I was able to have time see a little bit of the city. The most striking thing about Edinburgh to me was the stone bricks that everything seems to be built by. This gives the city a real medieval feel that we just do not see in the US. In the centre of the city, is a giant castle and the city seems to be surrounded by large snow covered hills. It really is a striking place. I also enjoyed looking around the various Scotch whisky shops, some of which, have a museum like collections. For an American, a trip to Scotland is not complete without eating the infamous Scottish national dish...Haggis. As a child, I was told stories of people eating terrible things out of sheep stomachs in Scotland (this was probably after the obligatory "what is a kilt" discussion), so at first I was a little afraid. However, I have to say Haggis is very tasty and nothing to be afraid of. I would even hazard to say that I could eat it on a regular basis. Luckily they had it every morning at my hotel!

InterPore Chapter Meeting in Edinburgh
In addition to the food and tourist attractions, the UK InterPore Chapter meeting was a great success and there were many interesting talks ranging from pore-scale simulations, swelling of bio-gels, and geotechnical porous media. It was a great opportunity to network across traditional bounds not just in terms of say engineers and mathematicians but across different application areas. As well as build a network of UK-based colleagues. It was interesting to see interaction between very different fields of study, for example the connections between swelling bio-gels, swelling of coals and clays under CO2 injection, and expanding bentonite in nuclear waste disposal. These problems give rise to challenging mathematical free-and moving boundary problems that Nottingham School of Mathematical Sciences has a particular expertise.

The week after I returned from the Edinburgh meeting we had an interesting seminar series in this area. It will be interesting to see what research impacts arise from these problems and techniques.

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