Vortex Ring Collisions and Transition to Turbulence

Vortex ring collisions are incredibly beautiful and also incredibly complex. Ryan McKeown of Harvard University explains his amazing experiments visualising colliding vortex rings and their transition to turbulence.

Every year the Gallery of Fluid Motion video contest features the newest and most beautiful research in fluid dynamics. Watch all of the Gallery of Fluid Motion videos here: http://gfm.aps.org.

This video is part of a collaboration between FYFD and the Journal of Fluid Mechanics featuring a series of interviews with researchers from the APS DFD 2017 conference. Sponsored by FYFD, the Journal of Fluid Mechanics, and the UK Fluids Network. Produced by Tom Crawford and Nicole Sharp with assistance from A.J. Fillo.

Featuring:

R. McKeown et al. “The emergence of small scales in vortex ring collisions” https://doi.org/10.1103/APS.DFD.2017….

Physical Review Fluids publication: https://doi.org/10.1103/PhysRevFluids…

Maths and the Media

Arriving at St John’s in 2008 to begin my study of mathematics, I was certain that within 4 years I would be working in the city as an actuary or an investment banker. Whilst I loved my subject, I saw it as means to obtain a good degree that would set me up for a career in finance. I’m not sure I could have been more wrong…

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My current journey began towards the end of my second year, where I found myself enjoying the course so much that I wanted to continue to do so for as long as possible. This led me to research PhD programmes in the UK and the US, and I was fortunate enough to be offered a place to study Applied Maths at the University of Cambridge in 2012. During my time at Oxford, I found myself straying further and further into the territory of applied maths, culminating in a fourth-year course in fluid mechanics – the study of how fluids such as water, air and ice move around. This ultimately led to my PhD topic at Cambridge: where does river water go when it enters the ocean? (If you’re interested to find out more I’ve written a series of articles here explaining my thesis in simple terms.)

As part of my PhD I conducted experiments, worked on equations and even took part in a research cruise to the Southern Ocean. It was on my return from 6 weeks at sea that I had my first taste of the media industry via a 2-month internship with the Naked Scientists. I would spend each day searching out the most interesting breaking science research, before arranging an interview with the author for BBC radio. It was great fun and I learnt so much in so many different fields that I was instantly hooked. Upon completion of my PhD I went to work with the Naked Scientists full time creating a series of maths videos looking at everything from beehives and surfing, to artwork and criminals. You can watch a short trailer for the Naked Maths series below.

My work with the BBC and the media in general ultimately led me to my current position as a Mathematics Tutor at three Oxford colleges: St John’s, St Hugh’s and St Edmund Hall. This may not sound like the media industry, but the flexibility of the position has allowed me to work on several projects, including launching my website and my YouTube channel @tomrocksmaths where I am currently running two ongoing series. In the first, Equations Stripped, I strip back the most important equations in maths layer-by-layer; and for the second series in partnership with the website I Love Mathematics, I answer the questions sent in and voted for by students and maths-enthusiasts across the world.

Alongside my online videos, I am also writing a book discussing the maths of Pokémon – Pokémaths – and have a weekly show with BBC radio called ‘Funbers’ where I tell you the fun facts about numbers that you didn’t realise you’ve secretly always wanted to know. I have also recently presented at conferences in the US and India and hold regular talks at schools and universities, including for the Oxford Invariants and the Maths in Action series at Warwick University where I faced my biggest audience yet of 1200.

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Looking back at my time at St John’s, I never would have imagined a career in the media industry lay before me, but the skills, experience and relationships that I formed there have undoubtedly helped to guide me along this path. I think it just goes to show that Maths is possibly the most universal of all subjects and really can lead to a career in any industry.

You can follow Tom on Twitter, Facebook and Instagram @tomrocksmaths for the latest updates.

Air Pollution Risk of Cooking Oil Droplets

Cooking oil in a frying pan can be dangerous when the ‘explosive’ droplets touch your skin, but new research shows that they also increase the risk of indoor air pollution if not properly ventilated. Interview with Jeremy Marston and Tadd Truscott at Texas Tech University and Utah State University.

Every year the Gallery of Fluid Motion video contest features the newest and most beautiful research in fluid dynamics. Watch all of the Gallery of Fluid Motion videos here: http://gfm.aps.org.

This video is part of a collaboration between FYFD and the Journal of Fluid Mechanics featuring a series of interviews with researchers from the APS DFD 2017 conference. Sponsored by FYFD, the Journal of Fluid Mechanics, and the UK Fluids Network. Produced by Tom Crawford and Nicole Sharp with assistance from A.J. Fillo.

Play Nice!

Whoever said having fun is more important than winning was not a game theorist. Game theorists are mathematicians who study games, and how to win them. But they aren’t just interested in Snakes and Ladders – game theory also involves studying ‘games’ like nuclear standoffs, trade wars and even the competition of species as they evolve.

New research from the Institute of Science and Technology in Austria (http://dx.doi.org/10.1038/s41586-018-0277-x) might help us to use game theory for environmental good. Their findings look at perhaps the single most important problem we face in looking after the environment – ‘the tragedy of the commons’.

The tragedy of the commons plays out all around us, and relates to situations where everybody stands to benefit from damaging a useful shared resource. Everybody in the office exploits the ‘commons’ of the biscuit tin by taking a biscuit, but nobody can be bothered to go out and buy a new packet to keep the tin full. Eventually, the tin is empty, and everyone has to endure life without biscuits whilst someone looks for more. Such pointless suffering could have been avoided if only someone had acted sooner!

In a more serious setting, the tragedy of the commons can lead to catastrophic results. Take deforestation – the shrinking of the world’s forests as we use trees faster than they can grow back. It is in the individual interests of each logging company to spend all their time chopping down trees (which makes them money) and to waste none of it replanting them (which doesn’t). At least, in the short term. But over time, this clearly won’t work – the ‘commons’ of the world’s forests will be so damaged that everyone will lose out. Bad news for all you atmosphere fans out there.

The new research uses game theory to study the tragedy of the commons, to try and understand what we can do to prevent it. To stick with the logging example, the researchers treat logging companies as players competing in a series of very simple games, over and over, learning each other’s tactics. Each game is just a matter of choosing one of two options: Chop down trees without bothering to replant them, or take the time to replant them as well. Each time the choice is made, the company gets a reward depending on what they picked; they will get a bigger reward if they don’t use any of their time replanting. It looks like companies that are perfectly happy to drop-kick Dr Seuss’ orange defender-of-the-trees, the Lorax, are going to do better than their greener rivals.

At least, initially. The key to the new research is that in it, the games that have already been played affect the rewards up for grabs in the next game. If you keep choosing not to replant trees, then you may do better than your opponents in each game, but you’ll gradually make the rewards smaller and smaller as you start to run out of trees to cut down. So, you can’t just think about the profits to be won in today’s game – you have to think about what you’ll be playing for in tomorrow’s game too.

The researchers found that this makes a big difference to how companies will play. If previous games made no difference to the current game, then companies which don’t replant trees would do better than their replanting rivals. But, given that failing to replant the trees you cut down means worse prizes in the future, the companies which do replant end up doing a lot better than those that don’t bother. In other words, it pays to play nice.

The one catch to this is that the prizes have to get significantly worse when you choose not to replant. So, in practical terms, these findings suggest ways to make the ‘game’ of logging less environmentally devastating – by changing the rules. For instance, governments could pass laws which force any companies failing to replant trees to pay an increased tax on any future trees they cut down (or maybe pay for the Lorax’s extensive pension plan). This makes logging more like the game the researchers studied, where past choices quickly and significantly affect future rewards. So based on the researchers’ findings, such a law would make sure that doing the right thing and replanting trees is the better choice.

Yes, game theory is about winning. But by figuring out which rules reward the sort of people who go out and buy more biscuits for the tin, we can make sure the ‘winning tactic’ for the world’s most dangerous games is to play nice.

Joe Double

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