JFM China Symposia: Hangzhou

I’m in China this week documenting the JFM Symposia ‘from fundamentals to applied fluid mechanics’ in the three cities of Shenzhen, Hangzhou and Beijing. Check out the CUP website for daily blog entries as well as some of my favourite video highlights from the scientific talks in Hangzhou below.

Detlef Lohse describes how a good scientist must be patient like a good bird-watcher as demonstrated by his experiments with exploding ice droplets

Hang Ding discusses falling droplets and shows a video of one hitting a mosquito

Quan Zhou presents some amazing visuals of Rayleigh-Taylor turbulence 

Tom Rocks Maths S02 E01

Tom Rocks Maths is back on Oxide – Oxford University’s student radio station – for a second season. The old favourites return with the weekly puzzle, Funbers and Equations Stripped. Plus, the new Millennium Problems segment where I tell you everything that you need to know about the seven greatest unsolved problems in the world of maths, each worth a cool $1 million. And not to forget the usual selection of awesome music from artists such as Rise Against, Panic at the Disco, Thirty Seconds to Mars – and for one week only – Taylor Swift. This is maths, but not as you know it…

Science Oxford Interview: From Togas to Tattoos…

I was interviewed by Autumn Neagle at Science Oxford about my toga-clad exploits in FameLab and the meaning of my maths-based tattoos… You can read the full article here.

What did you enjoy most about the FameLab experience?

“I’d been aware of FameLab for a few years, but I’d never entered because I thought that you had to talk about your own research – and with mine being lab-based I didn’t think it would translate very well to the live element of the show. But, once I found out that I could talk about anything within the subject of maths then it was a whole different ball game and I just had to give it a go. I think my favourite part was actually coming up with the talks themselves, just sitting down and brainstorming the ideas was such a fun process.”

What did you learn about yourself?

“The main takeaway for me was the importance of keeping to time. I knew beforehand that I was not the best at ‘following the rules’ and I think that both of my FameLab talks really demonstrated that as I never actually managed to get to the end of my talk! This was despite practicing several times beforehand and coming in sometimes up to 30 seconds short of the 3-minute limit – I think once I’m on stage I get carried away and just don’t want to come off!”

What about post-FameLab – how has taking part made a difference?

“Well, I certainly now appreciate the comfort and flexibility of wearing a toga that’s for sure! But on a more serious note, I think the experience of being on stage in front of a live audience really is invaluable when it comes to ‘performing maths’ – and I say ‘performing’ because that’s now how I see it. Before I would be giving a lecture or a talk about maths, but now it’s a full-on choreographed performance, and I think taking part in FameLab really helped me to understand that.

Any tips for future contestants?

“It has to be the time thing doesn’t it! I think everyone knows to practice beforehand to ensure they can get all of the material across in the 3-minutes, but for me that wasn’t enough. I’d suggest doing the actual performance in front of a group of friends or colleagues because – if they’re anything like me – then the adrenaline rush of being on stage changes even the best rehearsed routines and you can only get that from the live audience experience.”

What are you up to now/next?

“I’ve actually just received an award from the University of Oxford for my outreach work which is of course fantastic but also completely unexpected! I really do just love talking to people about maths and getting everyone to love it as much as I do, so the plan is very much to keep Tom Rocks Maths going and to hopefully expand into television… I have a few things in the pipeline so watch this space.”

Are all of your tattoos science inspired and if so what’s next?

“Now that I’ve reached the dizzy heights of 32 tattoos I can’t say that they are all based on science or maths, but it’s definitely still one of the dominant themes. So far I’ve got my favourite equation – Navier-Stokes, my favourite shapes – the Platonic Solids, and my favourite number – e. Next, I’m thinking of something related to the Normal Distribution – it’s such a powerful tool and the symmetry of the equation and the graph is beautiful – but I’ve yet to figure out exactly what that’s going to look like. If anyone has any suggestions though do let me know! @tomrocksmaths on social media – perhaps we can even turn it into a competition: pick Tom’s next tattoo, what do you think?”

In your YouTube video’s #EquationsStripped you reveal the maths behind some of the most important equations in maths, and I noticed that you describe the Navier-Stokes equations as your favourite – why is that and perhaps most importantly can you solve them?

“My favourite equations are the Navier-Stokes equations, which model the flow of every fluid on Earth… Can I solve them? Not a chance! They’re incredibly complicated, which is exactly why they’re a Millennium Problem with a million-dollar prize, and my idea with the video and live talk is to try to peel back the layers of complexity and explain what’s going on in as simple terms as possible.”

Does that mean that anyone can follow your video?

“The early parts yes absolutely, I purposefully start with the easier bits – the history, the applications, and then gradually get more involved with the physical setup of the problem and finally of course the maths of it all… And that’s pretty much where the idea to ‘strip back’ the equations came from – I thought to myself let’s begin simple and then slowly increase the difficulty until the equation is completely exposed. Being the ‘Naked Mathematician’ the next move was pretty obvious… as each layer of the equation is stripped back, I’m also stripping myself back until I’m just in my underwear – so almost completely exposed but not quite!”

Where did the whole idea of ‘stripping’ equations come from?

“I suppose I don’t really see it as ‘stripping’ per se, it’s there for comedic effect and really to show that maths is not the serious, boring, straight-laced subject that unfortunately most people think it is. Stripping for the videos is fine – it’s just me alone with my camera, but then earlier this year I was asked to give a live talk for the Oxford Invariants Society and they were very keen to emphasise that they wanted to see the Naked Mathematician in the flesh – quite literally!”

And how did it go?

“Well, barring some slightly awkward ‘costume changes’ between the layers of the equation – I went outside for the final reveal down to my underwear for example – it was good fun and definitely something I’d be keen to try out again… Perhaps maybe even an Equations Stripped Roadshow. I’m keen to try out anything that helps to improve the image that people have of maths.”

Navier-Stokes: one equation to rule them all

A leading Millennium Prize Problem is the Navier-Stokes equation, which, if solved, could model the flow of any fluid – that means how aeroplanes navigate the skies, how water meanders in a river and how the flow of blood courses through your blood vessels… Understanding these equations in more detail will lead to scientific advances in all of these fields: better aircraft design, improved flood defences, and better drug delivery in the body. Fluids expert and mathematician Keith Moffatt took me down to the deep dark depths of Cambridge’s maths lab…

  • For most fluids, including air and water, the Navier-Stokes equations are based on Newton’s Laws and were first written down in the 19th century
  • The millennium problem is to answer the question of whether or not the equations can become infinite
  • It cannot be solved with a computer because a computer programme will break down before the singularity at infinity is reached
  • A real-world example is when two tornado-like vortices collide and undergo a process called ‘vortex reconnection’

You can listen to the full interview for the Naked Scientists here.

And you can read more about the Navier-Stokes equations and all of the Millennium Problems here.

Equations Stripped: Navier-Stokes

A new series where I strip-back some of the most important equations in maths layer by layer so that everyone can understand…

First up is Navier-Stokes which models the flow of any fluid on Earth…

Navier-Stokes Equations

Millennium Problem number four is my favourite, hands down. I’m probably not supposed to be biased but when you have an equation tattooed on your body the rules change. The Navier-Stokes equations describe the flow of every fluid you can possibly think of: rivers, water from a tap, waves, wind, air flow around an aeroplane, ice in glaciers, ketchup, honey dripping off a spoon, blood in your body… I could go on forever.

The fact that these equations can do all of this is great – it shows that things in nature behave similarly, and we may actually understand some of it. But, there is a downside. To be able to describe such a variety of different fluids all at once, these equations are super-complex. I’m talking the plot of Inception complex. And just like no-one really understands Inception (no matter what they might tell you), mathematicians don’t understand all the little intricacies of the Navier-Stokes equations.

The easiest way to think about it is using what we call a singularity. It might sound complicated but I’m going to explain it step-by-step so stick with me. Start with a number, let’s say 2. Divide 1 by 2 and you get 1/2. Now take a smaller number, say 1/4 and divide 1 by it – ‘dividing by a fraction is the same as multiplying by it upside down’ (sorry, I’m just hearing the voice of my primary school teacher). The answer is 4 though. Now take a smaller number, say 0.1 and divide 1 by it. You get 10. Take a smaller number 0.01 and divide 1 by it, you get 100. Continue this: divide 1 by smaller and smaller and smaller numbers and you will get a bigger and bigger and bigger answer. So what happens when you divide 1 by 0? Maths breaks is the answer, but we can think of it as infinity or in our case a singularity.

Singularities occur in nature too with perhaps the most famous example being a black hole. These guys are so complicated that even Stephen Hawking struggles to understand what’s going on, which gives you an idea of why singularities are such a nuisance. Going back to the Navier-Stokes equations and the motion of fluids, my favourite example involves bubbles. Let’s do a little experiment. Take two circular pieces of wire and holding them close together dip them in soapy water. Imagine those little bottles of bubbles you used to get as a kid, and the plunger thing with the circle bit on the end… that. Well, two of them close together. The idea is that when you hold them close together, dip them in soap and then take them out a bubble will form between the two. It should form a cylinder shape – like the centre of a toilet roll. As you move the two circular wires apart the bubble will stretch and grow taller (think toilet roll to kitchen roll). You can keep moving the wires further and further apart and the bubble gets longer and longer and then POP! You’ve moved them too far apart and the bubble breaks.

Thinking about this mathematically is a nightmare. It makes sense at first, the wires move further apart and the size of the bubble grows. Increase the distance between the wires and the bubble size increases – a nice simple mathematical relationship. Until you reach the point where the bubble pops. At this instant the increase in the distance between the wires causes a sudden and incredibly fast decrease in the bubble size to zero. It’s so fast you can call it infinite. This is your singularity. The video below shows a great example of the experiment I’ve just described and shows the moment where the bubble size suddenly goes to zero.

As I said above the Navier-Stokes equations model the flow of any and every fluid – this means they describe the bubble popping madness we’ve just looked at and most importantly the singularity. We don’t know how or why or what is going on with these guys – again, think of black holes – and that is the Millennium Problem. Can we improve our understanding of these equations? In Lord of the Rings it was one ring to rule them all, in the maths of fluids the Navier-Stokes equations are your ruler… now bow down and make some bubbles.

 

You can listen to me interviewing Professor Keith Moffat about the problem here.

I’ve written a series of articles on each of the 7 Millennium Problems which can be found here.

 

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