STEM for Britain Competition

On Wednesday March 13th I’ll be presenting my research to MP’s at the Houses of Parliament in the final of the STEM for Britain Competition. You can find my research poster on modelling the spread of pollution in the oceans here.

Read coverage of my entry by the Oxford Maths Institute, St Edmund Hall, St Hugh’s College and the Warrington Guardian. The press release from the London Mathematical Society is also copied below.

Dr Tom Crawford, 29, a mathematician at Oxford University hailing from Warrington, is attending Parliament to present his mathematics research to a range of politicians and a panel of expert judges, as part of STEM for BRITAIN on Wednesday 13th March.

Tom’s poster on research about the spread of pollution in the ocean will be judged against dozens of other scientists’ research in the only national competition of its kind.

Tom was shortlisted from hundreds of applicants to appear in Parliament.

On presenting his research in Parliament, he said, “I want to bring maths to as wide an audience as possible and having the opportunity to talk about my work with MP’s – and hopefully show them that maths isn’t as scary as they might think – is fantastic!”

Stephen Metcalfe MP, Chairman of the Parliamentary and Scientific Committee, said: “This annual competition is an important date in the parliamentary calendar because it gives MPs an opportunity to speak to a wide range of the country’s best young researchers.

“These early career engineers, mathematicians and scientists are the architects of our future and STEM for BRITAIN is politicians’ best opportunity to meet them and understand their work.”

Tom’s research has been entered into the mathematical sciences session of the competition, which will end in a gold, silver and bronze prize-giving ceremony.

Judged by leading academics, the gold medalist receives £2,000, while silver and bronze receive £1,250 and £750 respectively.

The Parliamentary and Scientific Committee runs the event in collaboration with the Royal Academy of Engineering, the Royal Society of Chemistry, the Institute of Physics, the Royal Society of Biology, The Physiological Society and the Council for the Mathematical Sciences, with financial support from the Clay Mathematics Institute, United Kingdom Research and Innovation, Warwick Manufacturing Group, Society of Chemical Industry, the Nutrition Society, Institute of Biomedical Science the Heilbronn Institute for Mathematical Research, and the Comino Foundation.

How to build a river in the lab

My thesis is based on experiments. A weird thing for a mathematician to say you might think, but that’s the truth. It was always planned to be experimental in nature – it even says so in the title – and that’s because it isn’t practical to go to the nearest large scale river outflow (for my work that would be the Rhine in the Netherlands) and start trying to measure things. Fieldwork works well on a Geography trip: you put your wellies on and start splashing around in a stream, measuring the depth with a metre ruler and the speed of the stream by timing a little paper boat as it sails downstream… But things aren’t so easy when you’re talking about a river several kilometres wide and tens of metres deep. The bigger rivers are harder to measure, but the big rivers are precisely the ones that we need to look at, because they’re the only ones big enough to be affected by the earth’s rotation. But we’ll come to that. First up, how do we recreate a big river in the lab?

The trick is to scale things down, as you may have guessed, but there’s a little more to it than just building a scale model of a river. Those little wooden models of a city or building that architects use to help see how their plans will come to life are scale models of the real thing: they are built the same, just with all measurements at a ratio of 1:500 say of the real distances. For example, if a real-life football pitch is 100m in length and 75m wide, then for a 1:500 scale model it would be 20cm long and 15cm wide. A scale model is a good idea in principal, but when working with rivers that are 1km wide and 10m deep, once you scale it down to lab-size, your depth is about as thin as a piece of paper, which isn’t practical. We have to be a little cleverer as mathematicians and think about what properties of the river are the most important and then only include those in our lab model.

I’ll give you an example. Let’s suppose we are trying to work out how fast Usain Bolt travels when he runs the 100m. For ease of the numbers, we can say he runs 100m in 10.0 seconds (a slow day for Usain – he’d had a few too many chicken nuggets before the race). There are many other factors that will affect his speed:

  • The wind was blowing at a speed of 1m/s against him
  • It was raining
  • He was wearing a waterproof coat (he forgot to remove it)
  • His bodyweight was 2kg higher than normal (those damn chicken nuggets)
  • One of his shoes was missing a spike
  • The race was in Brazil

We know that all of these things will affect Usain’s speed, but which do we actually think are important enough to include them in our model? If we ignore them all then at a first guess, we can just use the speed = distance/time triangle from school which gives 100/10 = 10m/s. This would be a first order estimate using just two properties: time and distance. If we want to include more information and get a more accurate answer, then maybe we can include the wind speed: 1m/s against him means he must run at 11m/s to cover 100m in 10 seconds. This is an increase of 10% on our first estimate of his speed, and so probably quite important. Because of the direction of the wind the rain will act against him too, though probably by only a very small amount. The coat will increase the air resistance slowing him down, but again probably quite small.

The key point here is that there are many factors that will affect the speed of Usain Bolt as he’s running the 100m, but as mathematicians our job is to figure out which ones are the most important and to only consider those. If we tried to model every small effect things would get very complicated very quickly and we don’t want that (trust me I’ve tried). Simple is good – so long as you don’t ignore the important bits…

For Usain’s speed we can probably keep the distance, time and the wind speed and that’s about it. Even if we included everything else I doubt the value would change very much from 11m/s, certainly by less than 10% which is a nice acceptable error that we can live with. For scaling rivers down to work with them in the lab we have to do the same thing: pick the important parts of the problem and ignore the rest. The key thing is picking the right bits – which we’ll come onto next time.

 

All of the articles explaining my PhD thesis can be found here.

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