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I'm Julie Yeomen's, head of theoretical physics. Thank you very much for joining us for the Trinity Turn 21 morning theoretical physics.

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It's great. We really appreciate your interest in in the department and and what we're doing.

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And we're very much looking forward to talking to you. We keep keeping going despite the pandemic.

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We're looking forward a lot to being back in the Beecroft soon,

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but it's it's possible to do almost theoretical physics, like when we're we're actually.

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Most is the chance encounters in the discussion pods.

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And the students being really close to each other so they can help each other.

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Today, we've got three leading theoretical physicists who are going to show you that

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hydrodynamics is a lot more than plumbing and just sloshing around in the bath.

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Two of us, because of us, manage to cope with science during the pandemic.

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And bringing up young babies. And so if they're a bit sleepy, forgive them.

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Housekeeping, please. Can you put questions in the question and answer session and then I'll pass them onto the speakers at the end of the talks?

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We're sorry we can't talk to you in person because of the numbers, but we hope to see many of you in the breakout rooms afterwards.

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I'll give more details of how to do that at the end. So our first speaker is Professor Steve Simon.

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Steve came to Oxford in 2009 from Bell Labs in the USA.

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He's currently a research professor in the Rudolf Pottle Centre. And he's professorial fellow at Somerville.

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Steve's a condensed matter physicists, and he specialises in topological aspects of strongly correlated electronic systems and quantum computation.

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Steve is famous for his book, this one. This is the Oxford solid steak basics.

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And if you want something to do in lockdown and want to do a bit of revision, this is a good place to start.

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So thank you very much, Steve. Over to you. OK. Thank you.

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Let me share my screen. This will work. Good.

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Can you see the screen and hear me? Yep, that's fine.

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Great. OK. So, as Julie said, the subject of the morning is this hydrodynamics.

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And the subject of my talk is, is why how genetics and you ask a question like that.

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It's good to ask the reverse question at the same time. Why not?

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Rethink of how dynamic we think of phenomena that we might see every day, like this kind of phenomenon you might see in a bathtub.

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And by this time we've seen it so many times, it's hardly surprising you might have to think of phenomena in a bigger bathtub.

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But again, this is something that's very, very familiar. However, highjacked dynamics can still do some things that are extremely surprising.

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Here's an example. This is a river ice block that runs through the middle of Munich.

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And it has this Perman standing wave right in the middle of it. And if you're very talented and look deprave, you can even even surf on it.

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This phenomenon is known as a hydraulic jump.

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It occurs when there's an obstruction to a flow and the velocity of the flow is greater than the upstream speed of the way.

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And so the wave is sort of trapped here in this standing static position.

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Here's another phenomena that looks like it. It probably shouldn't work, but it is. This is not a motorised device.

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This guy is just gliding along on on this little aerofoil hydrofoil type thing that's holding him above the water.

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This probably is a lot harder than it looks, but he can glide for very, very long distances without falling down into the water.

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He gets enough lift from a gliding along to keep him him up.

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And then when he runs out of momentum, he can actually give himself a lot of forward momentum just by jumping up and down on this device.

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I'd love to love to try this, especially in this beautiful environment of Hawaii.

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And in a second,

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you'll see him jump up and down and give himself some more for momentum and essentially keep going almost indefinitely forward on this on this device.

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Most of what we think of a modern high dynamics is summarised in the now of your stocks equation or small generalisations of this equation.

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It's a not too frightening looking equation. It has terms like the density, the velocity, the pressure, viscosity in it.

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But from a mathematical standpoint, it's actually an extremely challenging equation to say things about.

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The turn of the millennium, the Clay Mathematics Institute isolated seven problems viewed to be the most important problem in mathematics.

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And this is a problem than before. If you can solve this problem by the end your strokes equation, you will win a million dollars.

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And so far, millions managed to do it.

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The question is about the net of your Stokes equation is given some initial conditions for the NATO stokes equation.

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Do so solutions always exist? And are these solutions always unique?

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This is still an unsolved problem. The problem is actually, interestingly enough, solved in two dimensions.

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Do the work of Ogilvy's in Skya in the 1960s, but it still remains unproven in three dimensions.

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So hydrodynamics applies to. Besides, besides just surfing on things.

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It applies to many, many other things. Vehicle drag is a classic example.

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You might say, wait a second, that's not hydrodynamics. That's actually aerodynamics.

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But to a physicist, we're not so concerned what fluid we're talking about.

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It's still governed by essentially the same same equation.

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So aerodynamics and hydrodynamics are put in the same category as has hydrodynamics.

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So vehicle drag is an example. Blood flow, slightly different fluid aircraft, again, aerodynamics.

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Here's one that's both aerodynamics and high dynamics is a seventy five foot long eight thousand

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kilogram sailboat managing to jump entirely out of the water during the America's Cup races.

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This is an interesting phenomena of hydrodynamics known as a Telvin Helmholtz instability and occurs.

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This is a picture of the clouds. It occurs when you have two layers of fluids moving with a relative velocity to each other.

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You get a finite wave vector and a finite wave length instability.

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Here you can see these periodic waves. This instabilities is also very closely related to the instability that causes waves on on the ocean.

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It's a little bit more complicated on the ocean.

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The thinking about weather and climate are hurricanes are inevitably a result of of high dynamics and aerodynamics as well.

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So here we have hydrodynamics over or Minmi lengths, native length scales from Micron's here, blood flow.

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Are we up to. Miles and miles in hurricanes. But that rather underestimates the applicability of of of hydrodynamics.

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So we can go to some really extreme situations like the quark blue on plasma.

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So we think of quarks as being the the objects that make up protons and neutrons in an other hadrons.

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But if you go up to very, very high temperatures or very, very high densities, they are no longer bound inside the nuclear enns, but rather form a.

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Continuum soup of of quarks and gluons. Rather than being being tied up together.

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So we can actually this quite well plasma is what the universe looked like in a few moments after after Big Bang.

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But we can study these quark room plasmas in in modern accelerators like Rick at Brookhaven or the LHC in France and Switzerland.

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So this is done as you take two big nuclei like like gold nuclei either or are lead nuclei.

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You accelerate them to ninety nine point nine nine five percent the speed of light and you smash them into each other.

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And that gives them energies.

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Are temperatures way up in the range of 10 trillion, Kelvin, and the nuclear arms melt and turn into this quark gluon plasma.

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And you get a droplet of this of this. Of this plasma. And the behaviour of this droplet.

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Has been studied and it's seen. And it turns out that it follows the laws of hydrodynamics.

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And this is on a length scale of ten to the minus 40 metres, the size of a nucleus and the energy scale.

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We have it 10 trillion Kelvin over it in a very different length scale.

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We can look at the interstellar medium, the gases and ions in things like a nebula in outer space.

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This is the Carina Nebula. It's about 10000 light years away. The field of view in this in this picture is about 50 light years across.

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But by by studying the motion of the gases in outer space,

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we've managed to establish that that the dynamics of these gases is basically turbulent

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hydrodynamics up to like scales of about a thousand light years and then a very different scale.

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Again, there are experiments on cold trapped atoms at energies of less than a micro kelvin.

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The way this experiment works is you take a small amount of a droplet of these

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of these trapped atoms and then you release this droplet from it from a trap.

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And you see the expansion of the droplet and the equations, emotion that govern the expansion of this droplet, our genetic equations.

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So what we have here is how genetics, acting on energy scales,

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going from 10 to minus seven Kelvin to 10 to 13 Kelvin and length scales from ten to the minus 14 metres to 10 to the 19th metres.

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That's 20 orders of magnitude and energy and thirty three orders of magnitude in length.

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That's pretty impressive. So why is genetics so, so ubiquitous?

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So we might start by asking, well, where's hydrodynamics come from? It's a hard question, which I'll try to say something about them.

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Is your question is, is who does hydrodynamics come from? Well, when people talk about hydrodynamics and its history, we often start with Archimedes,

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although strictly speaking, he was really interested in Hydra's static's.

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But he did some marvellous work thousands of years ago, which we still have many his manuscripts, which are still quite beautiful.

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The next person to take Hydromatic seriously was probably Leonardo da Vinci.

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Now, if you've been watching the new Amazon TV series on Manado, which The Guardian called completely insipid.

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So that means I absolutely had to watch it. They get a lot of things wrong about.

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About DaVinci. I'm sure a lot of it's fictionalised.

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But one thing they do get right is that he was fascinated with the flow of water and he sketched over over various fluid, dynamic phenomena.

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This is sketch. He is actually showing a hydraulic jump. He has a fluid flow hitting an obstacle.

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And there's a a permanent standing wave at the position of the obstacle, just like in the video I showed in the in the second slide.

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He also managed to realise the importance of conservation of mass in the in the flow of water,

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although he didn't really understand the distinction between mass and volume. The next person, of course, Isaac Newton.

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All of modern physics relies on him. But the people who really broke open the field of fluid dynamics in the modern sense were banali and an oilor.

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Now, these two guys knew each other very well. They both grew up in Basel about the same time.

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They actually even shared an apartment in St. Petersburg where they were both junior professors when they were young.

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By the end of all his work is this manuscript. He wrote General Principles on the movement of Fluid.

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We pretty much understood how we should formulate hydrodynamics, so we pretty much understood enough about hydrodynamics to understand why.

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And Aerofoil generates lift. They didn't have aeroplanes back then or hydrofoils back then,

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but they did have things like bird wings and they could understand how a bird generates lift by flying through the air.

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Now, it was about. About 50 years later that we had.

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Your stocks equation in some sense. Of course, your stocks equation is very important.

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Bence. But in some ways, it's a sort of a minor correction to what Waler had managed to do.

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Incidentally, Oilor was almost completely blind when he wrote this work and he was almost completely blind for the last twenty five years of his life.

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He said it took away many of the distractions and it just enabled him to do more mathematics, which he did quite proficiently.

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So all of this was long, long before we knew that fluids were made up of microscopic particles.

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Now there is this thing called atomic conjecture, but people didn't really know if fluids were actually made up of of atoms or molecules at all.

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That really came with a kinetic theory of gases.

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And in the eighteen hundreds with Maxwell and Boltzmann, who really start to understand that fluids are made up of lots of smaller particles.

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But we don't want to really, if we can avoid it, we don't want to really think about our fluids as being made up of lots of little particles.

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We can use that. For inspiration. But what we'd really like to do is describe our fluids in a more macroscopic sense.

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So just to give you an illustration of how this works. What I'm going to do here is here's a histogram of the speed of all the particles

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in this in this box and in the histogram changes as a function of time.

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Let's start that the video over. So, OK, the particles are injected into the box.

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All of the particles, when they're injected, have the same speed. There's a big peak in the histogram.

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But then the particles start bumping into each other.

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And very quickly it comes to a static distribution known as the maximal Boltzmann distribution of particle speeds.

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Once this happens, we say that the particles have equilibrated or thermals.

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And after that, we could describe the system just with a couple of thermodynamic quantities.

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The temperature, the pressure, these kind of quantities, rather than describing the behaviour of every individual particle in in the box.

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So we point here is that we don't need to know the microscopic details of our fluid.

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We can just describe it with some gross from anomic quantities that we keep track of.

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So it doesn't really matter if our conventional thinking about a conventional fluid made up of atoms or our molecules like air or water,

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or if we're thinking about a quark do on plasma made up of quarks bumping into each other.

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Or we can think of a cold atom fluid or an electron fluid. These are all these fluids are are a little bit different from each other.

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For example, the electron fluid. The electrons are interacting via a long range coulomb interaction.

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Whereas in in air, the you can think of the debt and the oxygen or nitrogen molecules as being essentially halves of the spheres.

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But overall, there's a great similarity that we have lots of particles that bump into each other and come to some thermal equilibrium.

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We have electron ion fluids. We can have a fluid of gravitating stars.

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So in this case, we think of each individual star as being like an atom and they interact with each other via the gravitational force rather

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than bumping into each other with the electrical force or bendable sports or whatever other force we're thinking about.

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So this is a very general idea.

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It's rather ubiquitous as long as we have something made up of lots of individual particles that we can then think of as our fluid.

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So we're going to do what what Oilor and Bhanumati did.

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We just said we just say let there be a fluid. We don't care if the fluid is made up of what is made up of.

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We don't we don't need to have to think about the microscopic details, but we do need to know what the conservation laws are.

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Conservation laws are extremely important in all of physics and particularly so in in hydrodynamics.

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So when we think about a fluid like like air or water, there are three national conservation laws that come to mind.

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Conservation of mass. There's a mass density conservation energy. There's some energy density and conservation of momentum.

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There's a momentum density. Now, momentum is a vector.

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Whereas mass and energy are scalar. So it is slightly different from here.

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And these three conservation laws, they're not completely, wholly different fluids might have different conservation laws.

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For example, if you think about a relativistic fluid that energy and mass aren't really different,

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conservation laws are actually in the same conservation law. If you have things that very, very high energy,

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it's possible to pair produce particle antiparticle pairs by putting in energy and getting out mass just by equals C squared.

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If you have enough energy so up at relativistic energy scales,

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you don't have separate conservation of mass and conservation of energy that can be traded for each other.

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Whereas at regular energy scales, the world around us, you know, water flow and air flow, energy and mass are conserved separately.

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Once we we pin down what our conservation laws are, the way we construct our hydrodynamics is a conserve do with a picture.

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We imagine having some small piece of the fluid, which is usually called a fluid parcel,

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as if it's going to be delivered by the Royal Mail or something.

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And we're going to track what happens, this fluid parcel as you flow through the fluid.

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Now, the shape of the food parcel might change the volume.

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It might change if the if the fluid is compressible like like air as compared to the incompressible fluid.

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Like like water. We're going to track what describes this fluid parcel as you move through the fluid flow.

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Now, what's important is that the parcel is assumed to be in some sort of local equilibrium.

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So it could be described macroscopically in the sense that it has a local temperature.

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It has a local momentum. It has a local density.

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And then we just have to ask, how do these local quantities change?

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As you flow through the fluid so you can write down very easily a set of equations,

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a set of equations is appropriate for an incompressible fluid like like water.

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And what it says is that the DNC doesn't change as you flow through the through the fluid.

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The energy density doesn't change as we flow through the fluid and the momentum density does change.

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It's given the change the momentum is given by the force on on that parcel.

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This is just Newton's law change. Momentum equals force.

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Now, you may notice that I've written these D by DTD. These look like derivatives, but I've written them with Capital D.

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And this is what's known as a code moving or material derivative.

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And what it means is that you should put yourself in the reference frame of the flow as you ask what happens?

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What would you do? My duty is what what your change with time is in the reference frame of of the flows.

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So these three equations are the incompressible oilor equations drive by by Euler to describe fluid flows.

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Now oilor was was clever enough to be able to consider compressible fluids as well.

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It's not that much of a generalisation to consider the possibility that the volume that the density of those changes as you move along the flow.

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Now it was a few years later, 50 years later, that Nabatean stokes came along.

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And what they did is they added, so the next order corrections to this description and what's left out of this description is that it's possible

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for these conserved quantities to leave the fluid parcel in directions other than the flow direction.

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So, for example, that the if you think about the momentum inside this fluid price, all that momentum can be exchanged with the next parcel over.

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So there will be another parcel sitting just above this fluid parcel up up in this area.

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And momentum could be traded between the two food parcels as you move along the flow.

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That's not included in the oilor equation. But it is included Navia Stokes.

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And if you do that, if you include those kind of contributions,

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you get the viscosity terms and Nappier Stokes, which is left out of out of Euler's equation.

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So hydrodynamics is basically just the dynamics of the conserve quantities,

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you identify what the conserve quantities are, what the thermodynamic variables are.

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And you ask about what the dynamics of these these variables are over a scales which are larger than the scales for which you can describe them.

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A region is having a well-defined temperature, pressure and other conserved quantities.

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The crucial assumption is that, at least locally, everything can be reduced to just a few conserved or thermodynamic variables,

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things like tap, local temperature, local local pressure. We don't want to have to describe fluid as lots of individual particles,

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but rather want to describe it at least locally in terms of a density, pressure, temperature, mean velocity and these sort of things.

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In fact, these aren't even all independent of each other.

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There's an equation of state which will relate together several of these these quantities to each other.

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And depending on what particular food you're thinking about, the equation in the state might be might be different.

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So this gives us the catchphrase that you should have thermodynamics before hydrogen.

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And what this means is that before we can start talking about how dynamics,

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we should be able to talk about local densities or local pressures, local temperatures.

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Once we have that, we ask about how these quantities change as you flow through the through the fluid.

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Now. It turns out that this this catch phrase is and these laws, these very simple laws that I've written down here are generally hydrodynamics.

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They don't always work or they're always there can be exceptions to this.

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And some of the exceptions are exceptionally interesting.

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So one that you'll hear about in today's second talk from Bloomberg TV is the possibility that you have some some interesting modern

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systems where you have more than just a few conserved quantities that you can't describe the system locally just in terms of density,

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pressure and temperature and velocity, but rather, you need many, many more variables to describe it.

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And so you'll hear about that in the second talk. Now under a star nets.

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We'll discuss that. Sometimes you can have hydrodynamics before thermodynamics that even though your system is not equilibrated locally,

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it hasn't come to some sort of thermodynamic equilibrium. It can't be described in terms of maximal Bozeman distribution.

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It doesn't have a well-defined pressure, doesn't have a well-defined temperature.

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Nonetheless, hydrogen nomics can still apply, which is a rather surprising result.

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So in the last few minutes, I'll I'll return to the original question, why hydrodynamics or why not?

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And and probably the best way to. To answer these questions is just a couple of examples.

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So I'm going to introduce a number of of examples of system is that either are or are not hydrodynamic.

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And explain why they are or are not. So the first example is the flow of stars.

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These pictures lie with the part that's a lie is the arrow that says you are here.

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And the reason this is lie is because it's obviously not a picture of our galaxy,

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because we haven't had the good fortune to leave our galaxy and look back and take a picture.

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This is a picture of the Andromeda Galaxy. It's about two one five million light years away as the closest major galaxy to us.

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And in a lot of ways, it's a proxy for our own galaxy. It's about the same same size, same shape.

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A lot of things that are very similar to our own galaxy. So so this arrow, if it were our own galaxy, would be pointing to roughly where we are,

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about halfway out the radius of the of the galaxy, a little less than halfway to be, to be honest.

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So we're somewhere around here in our galaxy. Now, the question you might ask is, is the flow of stars in in our galaxy or in the Andromeda galaxy?

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Is it hydrodynamic? And the answer is that, in fact, it's not.

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And the reason it's not is you can understand this by going back to the animation I showed you of

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clumping particles into a box in the first few moments when they pop the particles into a box.

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They did not have a maximal Boltzmann distribution. They were not describable with a simple temperature and pressure.

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And we had to wait until the particles bumped into each other and equilibrated or thermals

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until you could describe the system as having a well-defined temperature and pressure.

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And the problem is that since the beginning of of the galaxy, since the stars formed,

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the stars haven't bumped into each other enough in our part of the galaxy to have really come to a thermodynamic equilibrium.

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So we cannot use hydrodynamics to describe the flow of stars in our in our part of the of the of the galaxy.

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However, if you go close to the galactic nucleus way here in the middle, the density to stars is much, much higher.

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The stars are moving much, much faster than bumping into each other much, much more frequently and near the galactic nucleus.

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Things look a lot more. Arthur MONADIC then looks more like a maximal both my distribution.

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You can start thinking about genetic behaviour of stars in that in that region.

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The second example is flow of electricity. The first person to do experiments and to realise that electricity flows through

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metals was an amateur scientist by the name of Stephen Grey in in Kent.

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And this was. Was well before people like Benjamin Franklin started experiment experimenting with with electricity.

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Now, we might ask whether the electrons form a fluid and the fluid flows dynamically.

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And the answer is, in fact, in most materials, electrons do not flow hydroponically.

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And the reason they don't. Is because mostly what the electrons bump into is not other electrons.

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If you want to have a fluid that is made up of electrons,

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what you what you need to have is that the electrons are bumping into other electrons and they're exchanging energy and momentum with other electrons.

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And the problem is, in the most materials, the the electrons mainly bump into a impurities and lattice vibrations, what we call phone on.

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So you can think of it as being an open system where most of the momentum and energy

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is being lost to the to the lattice and not being exchanged with other electrons.

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So the electrons don't really form a fluid. We are fluid.

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The definition of a fluid is that you're exchanging energy momentum with the other particles within the fluid.

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But that's not happening here. And the difference in having a high dynamic versus a non high dynamic flow of

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electrons is illustrated by these two two pictures with Omec flow through a wire.

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You have a uniform velocity through the cross-section of the wire, whereas if you had had a fire hydrant flow, this is highly kinetic flow.

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You'd have a velocity which is much faster in the middle of the pipe than on the sides of the pipe.

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And the reason for this is because the only thing the electrons interact with these other electrons until they hit the boundary of the system.

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So the electrons are dragged by the boundary of the system. So the velocity goes to zero near the boundary.

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But then in the middle of the system, the electrons are not drag very much at all except with the neighbouring electrons and them.

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And they get dragged by the neighbouring electrons and they get dragged by the neighbouring electrons and so forth.

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So you can go very fast in the middle of the system and have to go very slow.

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Yeah, near the boundaries. Now, in 1963, the Soviet physicist Gerti pointed out that you could in principle get hydrodynamic electron flow.

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If your system was extremely clean. So you weren't bumping into immaturities all the time.

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And if you were at very low temperature, so you weren't bumping into latticed vibrations or phonons all the time.

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Now, others have proposed in the 60s it wasn't actually achieved until the 1990s.

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And the reason it had to wait so long is because we had to wait for the semiconductor industry to be able to make materials that

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were sufficiently free of impurities if the electrons could travel for very long distances before before hitting any impurity.

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So the main thing that in these semiconductor heteros structures, the main thing that the electrons bump into is other electrons.

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So the electrons amongst themselves form a nice fluid rather than always just bumping into the impurities.

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Rather surprisingly, in 2016, it was noticed that this is interesting family materials called Delphi sites.

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This is what the structure looks like. This is particularly with Palladium Cobalt eight.

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It's layers of palladium here in orange. Cobalt is inside these octahedron and an oxygen of the blue things on the blue small spheres.

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And that on the on the boundary of the hedra in these materials, for reasons that aren't completely understood, is still a topic of current research.

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The electrons, they don't bump into lattice vibrations. Almost all are.

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They don't seem to. And they flow very high dynamically. Now, one of the conjectures, which is rather interesting,

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is what you have is a fluid of both electrons and phonons that they flow together with the latest vibrations.

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You think of them as particles and they move with the electrons and the fluid of electron plus lattice vibration flow is completely freely,

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without and without intersect,

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without intersecting anything else except these other electron phone on combinations that move along through the material.

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The third example, this will be my last example, is that you can have a situation where you have two oppositely charged fluids in the same material.

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So a good example of this is graphene. Graphene is a single layer of carbon in this sort of honeycomb configuration.

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So I've written this as graphene because you can have single layer graphene, double layer graphene, triple layer graphene and so forth.

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At zero temperature, you have no charge carriers' free in these in these grafton's.

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But if you raise the temperature up a little bit, you can get free electrons and free holes.

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You excite an electron out of the valence band up to the conduction band, leaving a hole behind with a positive charge and electrons negative charge.

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So here's my animation of this. So you started zero temperature.

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You add a little energy, you make an electron whole pair, electron positron pair.

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If you a high energy physicist.

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They move apart from each other and then you can do this many times, so you get a fluid that's made up of of of electrons and holes,

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and you really need to think of these as being two separate fluids, because if you put an electric field on the system,

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the electrons will flow one way and the holes will flow the opposite way.

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So we have a system with with two almost conserved densities.

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So we have two fluid hydrodynamics and momentum and energy can be exchanged between the two fluids.

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And this is a topic that my group has been studying all over the last couple of years,

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have been what beautiful experiments on these particular systems isn't that I should say that the

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discovery of graphene was awarded Nobel Prise a few years ago to Andrew got Geim and Cusi no Aslaug,

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who are now in Manchester.

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A very analogous example is the hydrogen plasma you get on just outside of the sun and the corona, the the corn on the sun is is extremely hot.

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It's much, much hotter than the surface of the sun. Actually, the region outside of the sun.

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And we like to think of hydrogen as being electron bound to proton.

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But it is energy scales with so, so hot.

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The electron comes from the block proton and you can think of the electrons and protons as travelling is two completely different fluids,

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of course, on on the sun. It's not just hydrodynamics, it's magneto hydrodynamics because magnetic fields,

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electric fields are extremely important to the flow of these of this plasma.

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So I'm going to end with some images taken from the Solar Dynamic Observatory.

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That's a satellite that's been up for about about 10 years.

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And you can see these these whirling fluids of of plasma on on the surface just above the surface of the sun in the corona.

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And we did show that again. And it's sort of it looks like a whirlpool or a vortex spinning around.

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And you can see it definitely looks like a fluid flow.

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In fact, the Solar Dynamics Observatory has has has observed many fluid flow phenomena on the sun,

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including Kelvin Helmholtz instabilities that the thing that I showed you that occurs in the clouds and also creates waves on the ocean.

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Credit to the Goddard Space Flight Centre. So I'll end there with a quick summary of the ideas that thermodynamics comes first.

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Do you want to equilibrate a system of many pieces and then you can ignore the underlying

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particles and they just describe it with some dramatic quantities like like temperature,

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pressure, density. And then once you know what the what the correct theorem quantities are,

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you study the dynamics of the conserved are almost conserved quantities, and that gives you the hydrodynamics.

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And this general idea of how we study things applies over many, many or is of magnitude.

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And I'll stop there and take take questions. Steve, thank you very much indeed for that.

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Questions coming in and feeds everybody put questions in the Q&A, I should say.

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I read the questions. I was going to read out loud. Go ahead.

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Go ahead. Yeah. Yeah. We got some questions from experts here.

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I just wanted to say, if you're not the next, but it's still absolutely fine to to to ask questions.

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We were talking about astrophysics, so that's thought that Martin Lamming says it's an interesting point about astrophysical hydrodynamics.

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And that was actually before you you came back and talked about when hydrogen IMX works or not.

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He said that the kulam mean free path in nebulae is often very much greater than the system sized.

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So the hydrodynamic approximation shouldn't work. Particles are confined by plasma, not hydrodynamic turbulence.

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Are they? And does the micro physics matter? I came back.

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Andre, in case you need a hand with this one. Well, I.

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What I was going to punt on this this question. I think it's American football expression, meaning give up.

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But I'll tell you what I do know is I'm not an astrophysicist or expense matter physicist.

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And so I was obviously talking a little bit outside of my my expertise.

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But what I do know when I read these papers. A few years back, we had a nice talk from Michael Barnes about.

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About turbulence and what is what they do know about about the the nebula, plasmas and Nebula.

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Is that the the the velocities of particles follow kamangar of turbulence, scaling up to very,

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very long length scales, up to a thousand thousand not light years in in in Nebula and interstellar gas.

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So so that is is it established that it's true that when you have when you need plasmas are more complicated, then then things like like water.

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And it so, so it does get more complicated.

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But they do have the Komaroff turbulent genetical scaling.

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Great. OK. Do you want to add anything to that? Yes, maybe just just a few your sentences.

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So more generally. Despite the fact that that mix is a very universal description of fluid gases and similar substances.

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It's not guaranteed that for a given system you do have a hydrodynamic regime and let alone kinetic energy.

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So if somebody comes to you with, for example, Hamiltonian or a system, a microscopic microscopic system and asks,

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can you prove theoretically that there is a hydrodynamic regime in this system, the answer currently is we don't know.

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So there are some criteria that allow us to say in which in which domain of parameters you may expect higher than increasing.

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But derivation, so denervation in some cases is possible.

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The kinetic beauty within a certain within a certain sort of domain of applicability.

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But generically, for a generic system, the first thing you have to ask whether or not your system has a dynamic equilibrium.

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So before asking question about how Goodlett Hydrodynamics, you have to ask a question.

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There are not a system at all has a global from a dynamic equilibrium.

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And on top of that, perhaps you have a hybrid named Christina and somebody in some cases.

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So it's a it's a rather it's a rather subtle and complicated question.

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So it's not guaranteed a priority, but a given system, the kinds of hydrodynamic description.

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Thanks, Andre. It's a really good answer. Thank you. Next on stage, the next one is is also going to challenge you a bit because this is epidemiology.

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OK. Thinking about microscopic to thermodynamic dynamic shift of viewpoint.

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So going from multiple particles to a few quantities, is there any relation to epidemiological modelling techniques?

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Oh, boy, that's that's a good. My brother's an epidemiologist. I should I should chat with him.

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Tricky way. It's tricky, I'm not sure. I mean. I was wondering about bacteria, because you can think of bacteria as fields,

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but I think it's a bit different because they're too big to be thermodynamic. Yeah, I don't know.

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I mean, I think year in especially in the in the in the post-Soviet era,

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a lot of physicists who work on complex systems got very interested in epidemiological

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modelling and then have thrown a lot of modern techniques of of complexity,

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kinetic theory and statistical mechanics at that, at epidemiology as well.

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I don't know to what extent these have been successful.

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I mean, a lot of the the the basic ideas of what you can do is just mechanically have already been done.

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And I think the problem that epidemiology is, is it's really quite complicated.

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And so I don't know the answer if there is if there's really a good a good mapping or not.

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But it's definitely something that people have tried and are continuing to try.

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Yeah. Right. Okay. So the next one is from Chris. Julie. Hello, Chris.

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Hi, Chris. Okay, thanks. Thanks, Steve. Great topic.

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You pointed out that the flow of stuff fluid in the galaxy gets less hydrodynamic as you move out from the centre.

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So is there a way to do the corrections to hydrogen yet?

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Yes. So this is essentially the same answer as Andre just gave that you can kinetic theory is more general than hydrodynamics.

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So you can you can you can formulate a kinetic theory which is which can handle things that the hydrodynamics can't quite can't quite handle.

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But at some point, you have things that get sufficiently poorly.

382
00:40:37,930 --> 00:40:44,670
You don't really have a good statistical description. And even kinetic theory starts to starts to fail.

383
00:40:44,670 --> 00:40:52,290
I mean, you can't do anything. You can't cut off the hierarchy's that you have to do you have to deal with.

384
00:40:52,290 --> 00:40:59,100
I mean, in principle, there's always some hierarchy where you can talk about two point correlation, see point causation for correlations and so forth.

385
00:40:59,100 --> 00:41:04,770
But in unless you you know, there's some randomness in this in the system,

386
00:41:04,770 --> 00:41:10,160
things having equilibrium to some extent, then you can never cut that off and it becomes unsolvable.

387
00:41:10,160 --> 00:41:16,080
But you can you can do better than then hydrodynamics with kinetic theory and principle.

388
00:41:16,080 --> 00:41:27,370
OK, so the next one is asking, why is equilibration necessary when definitions of density and local mean velocity and pressure are independent?

389
00:41:27,370 --> 00:41:31,820
So that's a very, very good, good, good question.

390
00:41:31,820 --> 00:41:42,580
And again, I'm going to give exactly the same the same answer that you can get by often with less than having a full equilibration.

391
00:41:42,580 --> 00:41:47,170
But things get more complicated. If you don't have full of Grobet you need to describe more about.

392
00:41:47,170 --> 00:41:52,180
You need to potentially describe more about your system if they're not fully equilibrated.

393
00:41:52,180 --> 00:41:55,240
If the system is fully calibrated, it is not fully calibrated.

394
00:41:55,240 --> 00:42:01,960
You may have to describe what are the other features locally that describe how it's not fully calibrated and can these

395
00:42:01,960 --> 00:42:08,480
features are these other quantities that you need to keep track of and can they flow from one region to another?

396
00:42:08,480 --> 00:42:13,530
It's essentially the same question, same answer as the previous one and the one before that.

397
00:42:13,530 --> 00:42:23,180
Yeah. Okay. For the next question is from Andrew Dilys. And he the quantum fluids which have superposition and other spooky quantum effects.

398
00:42:23,180 --> 00:42:27,130
Nice. How can you apply classical nubby a state play?

399
00:42:27,130 --> 00:42:33,550
In some cases you can't. So that's true with quantum fluids like I like called atom fluids.

400
00:42:33,550 --> 00:42:37,690
You can make Boase condensates and so forth and you can get some some quantum effects,

401
00:42:37,690 --> 00:42:42,220
interference effects that are completely not in classical Nabby or Stokes.

402
00:42:42,220 --> 00:42:49,750
So the experiment that I in some experiments that you may do can be described by Binaggio Stokes.

403
00:42:49,750 --> 00:42:56,680
But are there others, some effects which actually had a picture of a globular cluster in the same picture, in the same slide?

404
00:42:56,680 --> 00:43:01,600
I don't think the audience can see the question. Oh, so. So the question now.

405
00:43:01,600 --> 00:43:08,520
So Jonathan Holmes asks, what stars in the lobby lacklustre B in hydrodynamic equilibrium and at the end.

406
00:43:08,520 --> 00:43:11,680
Are you okay? I don't how I raised it.

407
00:43:11,680 --> 00:43:16,090
Unfortunate, but it was on the same slide as the as the one of the Andromeda Galaxy.

408
00:43:16,090 --> 00:43:22,780
I had the picture of the globular cluster M fifty four making it so globular clusters that they're much smaller than galaxies,

409
00:43:22,780 --> 00:43:27,850
about a million times fewer, fewer stars. But they,

410
00:43:27,850 --> 00:43:34,240
they do seem to be that the stars have crashed into each other enough that they

411
00:43:34,240 --> 00:43:40,990
seem to be close to a maximal bowsman distribution and thermodynamic equilibrium.

412
00:43:40,990 --> 00:43:50,820
So most Labriola clusters do fit the magnetic equilibrium description and you can use these three fanatic's and hydrodynamics.

413
00:43:50,820 --> 00:43:57,550
Describe them now. When when we gave these practise talks, James Behney corrected me, saying, well,

414
00:43:57,550 --> 00:44:04,030
it's not quite there in nomics because the stars at the very tail of the natural bozman distribution is always

415
00:44:04,030 --> 00:44:09,790
cut off because there's going to be a few stars that just escape the cluster altogether and fly off to infinity.

416
00:44:09,790 --> 00:44:18,130
So it's not exactly natural. Boltzmann, but it's it can get pretty close to Maxwell Boltzmann in globular clusters.

417
00:44:18,130 --> 00:44:25,090
So very good. Very good question. And it's I don't know a whole lot about astronomy and astrophysics, but I do know the answer.

418
00:44:25,090 --> 00:44:30,370
One question that I'm so glad to give it. How about the hydrogen that makes it gravitational waves?

419
00:44:30,370 --> 00:44:36,460
You know, if anyone's. Oh, boy, that's that's a really good question. I don't know the answer.

420
00:44:36,460 --> 00:44:43,330
I'd be surprised people haven't thought about this. I don't know who would be the people to to think about it.

421
00:44:43,330 --> 00:44:51,470
I mean, the thing is that that I'm going to take a guess here that the.

422
00:44:51,470 --> 00:44:55,270
You know, the good for most of our universe, the universe is pretty flat.

423
00:44:55,270 --> 00:45:06,870
And that and the gravitational waves are very small. You know, perturbs of ripple on top of the what is otherwise a a flat universe.

424
00:45:06,870 --> 00:45:10,800
Now, if if the ripples get get fairly substantial,

425
00:45:10,800 --> 00:45:16,980
then they can start bumping into each other and and interacting with each other and bouncing off of each other ice.

426
00:45:16,980 --> 00:45:23,720
And I'm sure the people who studied black holes and and more violent gravitational phenomena.

427
00:45:23,720 --> 00:45:29,370
I have thought about how gravitational waves interact with each other and whether they form a hyphenated side.

428
00:45:29,370 --> 00:45:35,570
I don't know the answer as to how heavy lambrix it gets and whether there's any regime.

429
00:45:35,570 --> 00:45:44,260
In which that's a reasonable description. I was, but I mean, certainly for the for the regions around us, not close to black holes.

430
00:45:44,260 --> 00:45:47,310
It it it's it would be appropriate.

431
00:45:47,310 --> 00:45:54,450
I would I would think it's just because there's not enough interaction between the gravitational waves with other gravity of graviton.

432
00:45:54,450 --> 00:46:02,600
So don't interact with the Grafton's very much. But in an extreme gravitational conditions, probably it's it's a reasonable thing to think about.

433
00:46:02,600 --> 00:46:06,830
But I don't know who who's done it. Right. We should stop there, Steve.

434
00:46:06,830 --> 00:46:12,020
I think because OK, time, I'm sure you'll answer the questions by typing.

435
00:46:12,020 --> 00:46:17,750
OK. How could you say I stick? Because what happened last time is that I don't much.

436
00:46:17,750 --> 00:46:22,230
Russia started answering the questions. All the speakers because he was getting through the list.

437
00:46:22,230 --> 00:46:27,320
Oh, OK. So I'll just do this with this one more. I'll get this one by typing Allah.

438
00:46:27,320 --> 00:46:32,724
So thank you very, very much for your. My pleasure.