I'm Julie Yeomen's, head of theoretical physics. Thank you very much for joining us for the Trinity Turn 21 morning theoretical physics. It's great. We really appreciate your interest in in the department and and what we're doing. And we're very much looking forward to talking to you. We keep keeping going despite the pandemic. We're looking forward a lot to being back in the Beecroft soon, but it's it's possible to do almost theoretical physics, like when we're we're actually.
Most is the chance encounters in the discussion pods. And the students being really close to each other so they can help each other. Today, we've got three leading theoretical physicists who are going to show you that hydrodynamics is a lot more than plumbing and just sloshing around in the bath. Two of us, because of us, manage to cope with science during the pandemic. And bringing up young babies. And so if they're a bit sleepy, forgive them.
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? 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. I'll give more details of how to do that at the end. So our first speaker is Professor Steve Simon. Steve came to Oxford in 2009 from Bell Labs in the USA.
He's currently a research professor in the Rudolf Pottle Centre. And he's professorial fellow at Somerville. Steve's a condensed matter physicists, and he specialises in topological aspects of strongly correlated electronic systems and quantum computation. Steve is famous for his book, this one. This is the Oxford solid steak basics. And if you want something to do in lockdown and want to do a bit of revision, this is a good place to start.
So thank you very much, Steve. Over to you. OK. Thank you. Let me share my screen. This will work. Good. Can you see the screen and hear me? Yep, that's fine. Great. OK. So, as Julie said, the subject of the morning is this hydrodynamics. And the subject of my talk is, is why how genetics and you ask a question like that. It's good to ask the reverse question at the same time. Why not?
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. 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. But again, this is something that's very, very familiar. However, highjacked dynamics can still do some things that are extremely surprising. Here's an example. This is a river ice block that runs through the middle of Munich.
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. This phenomenon is known as a hydraulic jump. 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. And so the wave is sort of trapped here in this standing static position. Here's another phenomena that looks like it. It probably shouldn't work, but it is. This is not a motorised device.
This guy is just gliding along on on this little aerofoil hydrofoil type thing that's holding him above the water. This probably is a lot harder than it looks, but he can glide for very, very long distances without falling down into the water. He gets enough lift from a gliding along to keep him him up. 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.
I'd love to love to try this, especially in this beautiful environment of Hawaii. And in a second, 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. 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.
It's a not too frightening looking equation. It has terms like the density, the velocity, the pressure, viscosity in it. But from a mathematical standpoint, it's actually an extremely challenging equation to say things about. The turn of the millennium, the Clay Mathematics Institute isolated seven problems viewed to be the most important problem in mathematics. 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.
And so far, millions managed to do it. The question is about the net of your Stokes equation is given some initial conditions for the NATO stokes equation. Do so solutions always exist? And are these solutions always unique? This is still an unsolved problem. The problem is actually, interestingly enough, solved in two dimensions. Do the work of Ogilvy's in Skya in the 1960s, but it still remains unproven in three dimensions. So hydrodynamics applies to. Besides, besides just surfing on things.
It applies to many, many other things. Vehicle drag is a classic example. You might say, wait a second, that's not hydrodynamics. That's actually aerodynamics. But to a physicist, we're not so concerned what fluid we're talking about. It's still governed by essentially the same same equation. So aerodynamics and hydrodynamics are put in the same category as has hydrodynamics. So vehicle drag is an example. Blood flow, slightly different fluid aircraft, again, aerodynamics.
Here's one that's both aerodynamics and high dynamics is a seventy five foot long eight thousand kilogram sailboat managing to jump entirely out of the water during the America's Cup races. This is an interesting phenomena of hydrodynamics known as a Telvin Helmholtz instability and occurs. This is a picture of the clouds. It occurs when you have two layers of fluids moving with a relative velocity to each other. You get a finite wave vector and a finite wave length instability.
Here you can see these periodic waves. This instabilities is also very closely related to the instability that causes waves on on the ocean. It's a little bit more complicated on the ocean. The thinking about weather and climate are hurricanes are inevitably a result of of high dynamics and aerodynamics as well. So here we have hydrodynamics over or Minmi lengths, native length scales from Micron's here, blood flow.
Are we up to. Miles and miles in hurricanes. But that rather underestimates the applicability of of of hydrodynamics. So we can go to some really extreme situations like the quark blue on plasma. So we think of quarks as being the the objects that make up protons and neutrons in an other hadrons. 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.
Continuum soup of of quarks and gluons. Rather than being being tied up together. So we can actually this quite well plasma is what the universe looked like in a few moments after after Big Bang. But we can study these quark room plasmas in in modern accelerators like Rick at Brookhaven or the LHC in France and Switzerland. So this is done as you take two big nuclei like like gold nuclei either or are lead nuclei.
You accelerate them to ninety nine point nine nine five percent the speed of light and you smash them into each other. And that gives them energies. Are temperatures way up in the range of 10 trillion, Kelvin, and the nuclear arms melt and turn into this quark gluon plasma. And you get a droplet of this of this. Of this plasma. And the behaviour of this droplet. Has been studied and it's seen. And it turns out that it follows the laws of hydrodynamics.
And this is on a length scale of ten to the minus 40 metres, the size of a nucleus and the energy scale. We have it 10 trillion Kelvin over it in a very different length scale. We can look at the interstellar medium, the gases and ions in things like a nebula in outer space. 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.
But by by studying the motion of the gases in outer space, we've managed to establish that that the dynamics of these gases is basically turbulent hydrodynamics up to like scales of about a thousand light years and then a very different scale. Again, there are experiments on cold trapped atoms at energies of less than a micro kelvin. The way this experiment works is you take a small amount of a droplet of these of these trapped atoms and then you release this droplet from it from a trap.
And you see the expansion of the droplet and the equations, emotion that govern the expansion of this droplet, our genetic equations. So what we have here is how genetics, acting on energy scales, 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. That's 20 orders of magnitude and energy and thirty three orders of magnitude in length. That's pretty impressive. So why is genetics so, so ubiquitous?
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. Is your question is, is who does hydrodynamics come from? Well, when people talk about hydrodynamics and its history, we often start with Archimedes, although strictly speaking, he was really interested in Hydra's static's. But he did some marvellous work thousands of years ago, which we still have many his manuscripts, which are still quite beautiful.
The next person to take Hydromatic seriously was probably Leonardo da Vinci. Now, if you've been watching the new Amazon TV series on Manado, which The Guardian called completely insipid. So that means I absolutely had to watch it. They get a lot of things wrong about. About DaVinci. I'm sure a lot of it's fictionalised. 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.
This is sketch. He is actually showing a hydraulic jump. He has a fluid flow hitting an obstacle. 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. He also managed to realise the importance of conservation of mass in the in the flow of water, although he didn't really understand the distinction between mass and volume. The next person, of course, Isaac Newton.
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. Now, these two guys knew each other very well. They both grew up in Basel about the same time. They actually even shared an apartment in St. Petersburg where they were both junior professors when they were young. By the end of all his work is this manuscript. He wrote General Principles on the movement of Fluid.
We pretty much understood how we should formulate hydrodynamics, so we pretty much understood enough about hydrodynamics to understand why. And Aerofoil generates lift. They didn't have aeroplanes back then or hydrofoils back then, but they did have things like bird wings and they could understand how a bird generates lift by flying through the air. Now, it was about. About 50 years later that we had. Your stocks equation in some sense. Of course, your stocks equation is very important.
Bence. But in some ways, it's a sort of a minor correction to what Waler had managed to do. 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. He said it took away many of the distractions and it just enabled him to do more mathematics, which he did quite proficiently. So all of this was long, long before we knew that fluids were made up of microscopic particles.
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. That really came with a kinetic theory of gases. And in the eighteen hundreds with Maxwell and Boltzmann, who really start to understand that fluids are made up of lots of smaller particles. 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.
We can use that. For inspiration. But what we'd really like to do is describe our fluids in a more macroscopic sense. 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 in this in this box and in the histogram changes as a function of time. Let's start that the video over. So, OK, the particles are injected into the box.
All of the particles, when they're injected, have the same speed. There's a big peak in the histogram. But then the particles start bumping into each other. And very quickly it comes to a static distribution known as the maximal Boltzmann distribution of particle speeds. Once this happens, we say that the particles have equilibrated or thermals. And after that, we could describe the system just with a couple of thermodynamic quantities.
The temperature, the pressure, these kind of quantities, rather than describing the behaviour of every individual particle in in the box. So we point here is that we don't need to know the microscopic details of our fluid. We can just describe it with some gross from anomic quantities that we keep track of.
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, or if we're thinking about a quark do on plasma made up of quarks bumping into each other. 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. For example, the electron fluid. The electrons are interacting via a long range coulomb interaction.
Whereas in in air, the you can think of the debt and the oxygen or nitrogen molecules as being essentially halves of the spheres. But overall, there's a great similarity that we have lots of particles that bump into each other and come to some thermal equilibrium. We have electron ion fluids. We can have a fluid of gravitating stars.
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 than bumping into each other with the electrical force or bendable sports or whatever other force we're thinking about. So this is a very general idea. 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. So we're going to do what what Oilor and Bhanumati did.
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. 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. Conservation laws are extremely important in all of physics and particularly so in in hydrodynamics. So when we think about a fluid like like air or water, there are three national conservation laws that come to mind.
Conservation of mass. There's a mass density conservation energy. There's some energy density and conservation of momentum. There's a momentum density. Now, momentum is a vector. Whereas mass and energy are scalar. So it is slightly different from here. And these three conservation laws, they're not completely, wholly different fluids might have different conservation laws. For example, if you think about a relativistic fluid that energy and mass aren't really different,
conservation laws are actually in the same conservation law. If you have things that very, very high energy, it's possible to pair produce particle antiparticle pairs by putting in energy and getting out mass just by equals C squared. If you have enough energy so up at relativistic energy scales, you don't have separate conservation of mass and conservation of energy that can be traded for each other.
Whereas at regular energy scales, the world around us, you know, water flow and air flow, energy and mass are conserved separately. Once we we pin down what our conservation laws are, the way we construct our hydrodynamics is a conserve do with a picture. We imagine having some small piece of the fluid, which is usually called a fluid parcel, as if it's going to be delivered by the Royal Mail or something. And we're going to track what happens, this fluid parcel as you flow through the fluid.
Now, the shape of the food parcel might change the volume. It might change if the if the fluid is compressible like like air as compared to the incompressible fluid. Like like water. We're going to track what describes this fluid parcel as you move through the fluid flow. Now, what's important is that the parcel is assumed to be in some sort of local equilibrium. So it could be described macroscopically in the sense that it has a local temperature.
It has a local momentum. It has a local density. And then we just have to ask, how do these local quantities change? As you flow through the fluid so you can write down very easily a set of equations, a set of equations is appropriate for an incompressible fluid like like water. And what it says is that the DNC doesn't change as you flow through the through the fluid. The energy density doesn't change as we flow through the fluid and the momentum density does change.
It's given the change the momentum is given by the force on on that parcel. This is just Newton's law change. Momentum equals force. Now, you may notice that I've written these D by DTD. These look like derivatives, but I've written them with Capital D. And this is what's known as a code moving or material derivative. And what it means is that you should put yourself in the reference frame of the flow as you ask what happens?
What would you do? My duty is what what your change with time is in the reference frame of of the flows. So these three equations are the incompressible oilor equations drive by by Euler to describe fluid flows. Now oilor was was clever enough to be able to consider compressible fluids as well. 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.
Now it was a few years later, 50 years later, that Nabatean stokes came along. 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 for these conserved quantities to leave the fluid parcel in directions other than the flow direction. 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.
So there will be another parcel sitting just above this fluid parcel up up in this area. And momentum could be traded between the two food parcels as you move along the flow. That's not included in the oilor equation. But it is included Navia Stokes. And if you do that, if you include those kind of contributions, you get the viscosity terms and Nappier Stokes, which is left out of out of Euler's equation.
So hydrodynamics is basically just the dynamics of the conserve quantities, you identify what the conserve quantities are, what the thermodynamic variables are. 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. A region is having a well-defined temperature, pressure and other conserved quantities.
The crucial assumption is that, at least locally, everything can be reduced to just a few conserved or thermodynamic variables, things like tap, local temperature, local local pressure. We don't want to have to describe fluid as lots of individual particles, but rather want to describe it at least locally in terms of a density, pressure, temperature, mean velocity and these sort of things. In fact, these aren't even all independent of each other.
There's an equation of state which will relate together several of these these quantities to each other. And depending on what particular food you're thinking about, the equation in the state might be might be different. So this gives us the catchphrase that you should have thermodynamics before hydrogen. And what this means is that before we can start talking about how dynamics, we should be able to talk about local densities or local pressures, local temperatures.
Once we have that, we ask about how these quantities change as you flow through the through the fluid. 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. They don't always work or they're always there can be exceptions to this. And some of the exceptions are exceptionally interesting.
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 systems where you have more than just a few conserved quantities that you can't describe the system locally just in terms of density, pressure and temperature and velocity, but rather, you need many, many more variables to describe it. And so you'll hear about that in the second talk. Now under a star nets.
We'll discuss that. Sometimes you can have hydrodynamics before thermodynamics that even though your system is not equilibrated locally, it hasn't come to some sort of thermodynamic equilibrium. It can't be described in terms of maximal Bozeman distribution. It doesn't have a well-defined pressure, doesn't have a well-defined temperature. Nonetheless, hydrogen nomics can still apply, which is a rather surprising result.
So in the last few minutes, I'll I'll return to the original question, why hydrodynamics or why not? And and probably the best way to. To answer these questions is just a couple of examples. So I'm going to introduce a number of of examples of system is that either are or are not hydrodynamic. And explain why they are or are not. So the first example is the flow of stars. These pictures lie with the part that's a lie is the arrow that says you are here.
And the reason this is lie is because it's obviously not a picture of our galaxy, because we haven't had the good fortune to leave our galaxy and look back and take a picture. 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. And in a lot of ways, it's a proxy for our own galaxy. It's about the same same size, same shape.
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, about halfway out the radius of the of the galaxy, a little less than halfway to be, to be honest. 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? Is it hydrodynamic? And the answer is that, in fact, it's not.
And the reason it's not is you can understand this by going back to the animation I showed you of clumping particles into a box in the first few moments when they pop the particles into a box. They did not have a maximal Boltzmann distribution. They were not describable with a simple temperature and pressure. And we had to wait until the particles bumped into each other and equilibrated or thermals until you could describe the system as having a well-defined temperature and pressure.
And the problem is that since the beginning of of the galaxy, since the stars formed, the stars haven't bumped into each other enough in our part of the galaxy to have really come to a thermodynamic equilibrium. So we cannot use hydrodynamics to describe the flow of stars in our in our part of the of the of the galaxy. However, if you go close to the galactic nucleus way here in the middle, the density to stars is much, much higher.
The stars are moving much, much faster than bumping into each other much, much more frequently and near the galactic nucleus. Things look a lot more. Arthur MONADIC then looks more like a maximal both my distribution. You can start thinking about genetic behaviour of stars in that in that region. The second example is flow of electricity. The first person to do experiments and to realise that electricity flows through metals was an amateur scientist by the name of Stephen Grey in in Kent.
And this was. Was well before people like Benjamin Franklin started experiment experimenting with with electricity. Now, we might ask whether the electrons form a fluid and the fluid flows dynamically. And the answer is, in fact, in most materials, electrons do not flow hydroponically. And the reason they don't. Is because mostly what the electrons bump into is not other electrons.
If you want to have a fluid that is made up of electrons, 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. And the problem is, in the most materials, the the electrons mainly bump into a impurities and lattice vibrations, what we call phone on.
So you can think of it as being an open system where most of the momentum and energy is being lost to the to the lattice and not being exchanged with other electrons. So the electrons don't really form a fluid. We are fluid. The definition of a fluid is that you're exchanging energy momentum with the other particles within the fluid.
But that's not happening here. And the difference in having a high dynamic versus a non high dynamic flow of electrons is illustrated by these two two pictures with Omec flow through a wire. 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. You'd have a velocity which is much faster in the middle of the pipe than on the sides of the pipe.
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. So the electrons are dragged by the boundary of the system. So the velocity goes to zero near the boundary. But then in the middle of the system, the electrons are not drag very much at all except with the neighbouring electrons and them. And they get dragged by the neighbouring electrons and they get dragged by the neighbouring electrons and so forth.
So you can go very fast in the middle of the system and have to go very slow. Yeah, near the boundaries. Now, in 1963, the Soviet physicist Gerti pointed out that you could in principle get hydrodynamic electron flow. If your system was extremely clean. So you weren't bumping into immaturities all the time. And if you were at very low temperature, so you weren't bumping into latticed vibrations or phonons all the time.
Now, others have proposed in the 60s it wasn't actually achieved until the 1990s. 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 were sufficiently free of impurities if the electrons could travel for very long distances before before hitting any impurity. So the main thing that in these semiconductor heteros structures, the main thing that the electrons bump into is other electrons.
So the electrons amongst themselves form a nice fluid rather than always just bumping into the impurities. Rather surprisingly, in 2016, it was noticed that this is interesting family materials called Delphi sites. This is what the structure looks like. This is particularly with Palladium Cobalt eight. 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.
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. The electrons, they don't bump into lattice vibrations. Almost all are. They don't seem to. And they flow very high dynamically. Now, one of the conjectures, which is rather interesting, is what you have is a fluid of both electrons and phonons that they flow together with the latest vibrations.
You think of them as particles and they move with the electrons and the fluid of electron plus lattice vibration flow is completely freely, without and without intersect, without intersecting anything else except these other electron phone on combinations that move along through the material. 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.
So a good example of this is graphene. Graphene is a single layer of carbon in this sort of honeycomb configuration. So I've written this as graphene because you can have single layer graphene, double layer graphene, triple layer graphene and so forth. At zero temperature, you have no charge carriers' free in these in these grafton's. But if you raise the temperature up a little bit, you can get free electrons and free holes.
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. So here's my animation of this. So you started zero temperature. You add a little energy, you make an electron whole pair, electron positron pair. If you a high energy physicist.
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, and you really need to think of these as being two separate fluids, because if you put an electric field on the system, the electrons will flow one way and the holes will flow the opposite way. So we have a system with with two almost conserved densities. So we have two fluid hydrodynamics and momentum and energy can be exchanged between the two fluids.
And this is a topic that my group has been studying all over the last couple of years, have been what beautiful experiments on these particular systems isn't that I should say that the discovery of graphene was awarded Nobel Prise a few years ago to Andrew got Geim and Cusi no Aslaug, who are now in Manchester. 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.
It's much, much hotter than the surface of the sun. Actually, the region outside of the sun. And we like to think of hydrogen as being electron bound to proton. But it is energy scales with so, so hot. The electron comes from the block proton and you can think of the electrons and protons as travelling is two completely different fluids,
of course, on on the sun. It's not just hydrodynamics, it's magneto hydrodynamics because magnetic fields, electric fields are extremely important to the flow of these of this plasma. So I'm going to end with some images taken from the Solar Dynamic Observatory. That's a satellite that's been up for about about 10 years. 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.
And we did show that again. And it's sort of it looks like a whirlpool or a vortex spinning around. And you can see it definitely looks like a fluid flow. In fact, the Solar Dynamics Observatory has has has observed many fluid flow phenomena on the sun, including Kelvin Helmholtz instabilities that the thing that I showed you that occurs in the clouds and also creates waves on the ocean.
Credit to the Goddard Space Flight Centre. So I'll end there with a quick summary of the ideas that thermodynamics comes first. Do you want to equilibrate a system of many pieces and then you can ignore the underlying particles and they just describe it with some dramatic quantities like like temperature,
pressure, density. And then once you know what the what the correct theorem quantities are, you study the dynamics of the conserved are almost conserved quantities, and that gives you the hydrodynamics. And this general idea of how we study things applies over many, many or is of magnitude. And I'll stop there and take take questions. Steve, thank you very much indeed for that. Questions coming in and feeds everybody put questions in the Q&A, I should say.
I read the questions. I was going to read out loud. Go ahead. Go ahead. Yeah. Yeah. We got some questions from experts here. I just wanted to say, if you're not the next, but it's still absolutely fine to to to ask questions. We were talking about astrophysics, so that's thought that Martin Lamming says it's an interesting point about astrophysical hydrodynamics. And that was actually before you you came back and talked about when hydrogen IMX works or not.
He said that the kulam mean free path in nebulae is often very much greater than the system sized. So the hydrodynamic approximation shouldn't work. Particles are confined by plasma, not hydrodynamic turbulence. Are they? And does the micro physics matter? I came back. Andre, in case you need a hand with this one. Well, I. What I was going to punt on this this question. I think it's American football expression, meaning give up.
But I'll tell you what I do know is I'm not an astrophysicist or expense matter physicist. And so I was obviously talking a little bit outside of my my expertise. But what I do know when I read these papers. A few years back, we had a nice talk from Michael Barnes about. About turbulence and what is what they do know about about the the nebula, plasmas and Nebula.
Is that the the the velocities of particles follow kamangar of turbulence, scaling up to very, very long length scales, up to a thousand thousand not light years in in in Nebula and interstellar gas. 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. And it so, so it does get more complicated. But they do have the Komaroff turbulent genetical scaling.
Great. OK. Do you want to add anything to that? Yes, maybe just just a few your sentences. So more generally. Despite the fact that that mix is a very universal description of fluid gases and similar substances. It's not guaranteed that for a given system you do have a hydrodynamic regime and let alone kinetic energy.
So if somebody comes to you with, for example, Hamiltonian or a system, a microscopic microscopic system and asks, can you prove theoretically that there is a hydrodynamic regime in this system, the answer currently is we don't know. So there are some criteria that allow us to say in which in which domain of parameters you may expect higher than increasing. But derivation, so denervation in some cases is possible.
The kinetic beauty within a certain within a certain sort of domain of applicability. But generically, for a generic system, the first thing you have to ask whether or not your system has a dynamic equilibrium. So before asking question about how Goodlett Hydrodynamics, you have to ask a question. There are not a system at all has a global from a dynamic equilibrium. And on top of that, perhaps you have a hybrid named Christina and somebody in some cases.
So it's a it's a rather it's a rather subtle and complicated question. So it's not guaranteed a priority, but a given system, the kinds of hydrodynamic description. 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. OK. Thinking about microscopic to thermodynamic dynamic shift of viewpoint.
So going from multiple particles to a few quantities, is there any relation to epidemiological modelling techniques? Oh, boy, that's that's a good. My brother's an epidemiologist. I should I should chat with him. Tricky way. It's tricky, I'm not sure. I mean. I was wondering about bacteria, because you can think of bacteria as fields, but I think it's a bit different because they're too big to be thermodynamic. Yeah, I don't know.
I mean, I think year in especially in the in the in the post-Soviet era, a lot of physicists who work on complex systems got very interested in epidemiological modelling and then have thrown a lot of modern techniques of of complexity, kinetic theory and statistical mechanics at that, at epidemiology as well. I don't know to what extent these have been successful. I mean, a lot of the the the basic ideas of what you can do is just mechanically have already been done.
And I think the problem that epidemiology is, is it's really quite complicated. And so I don't know the answer if there is if there's really a good a good mapping or not. But it's definitely something that people have tried and are continuing to try. Yeah. Right. Okay. So the next one is from Chris. Julie. Hello, Chris. Hi, Chris. Okay, thanks. Thanks, Steve. Great topic. You pointed out that the flow of stuff fluid in the galaxy gets less hydrodynamic as you move out from the centre.
So is there a way to do the corrections to hydrogen yet? Yes. So this is essentially the same answer as Andre just gave that you can kinetic theory is more general than hydrodynamics. 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. But at some point, you have things that get sufficiently poorly. You don't really have a good statistical description. And even kinetic theory starts to starts to fail.
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. 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. But in unless you you know, there's some randomness in this in the system, things having equilibrium to some extent, then you can never cut that off and it becomes unsolvable.
But you can you can do better than then hydrodynamics with kinetic theory and principle. OK, so the next one is asking, why is equilibration necessary when definitions of density and local mean velocity and pressure are independent? So that's a very, very good, good, good question. 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.
But things get more complicated. If you don't have full of Grobet you need to describe more about. You need to potentially describe more about your system if they're not fully equilibrated. If the system is fully calibrated, it is not fully calibrated. You may have to describe what are the other features locally that describe how it's not fully calibrated and can these features are these other quantities that you need to keep track of and can they flow from one region to another?
It's essentially the same question, same answer as the previous one and the one before that. Yeah. Okay. For the next question is from Andrew Dilys. And he the quantum fluids which have superposition and other spooky quantum effects. Nice. How can you apply classical nubby a state play? In some cases you can't. So that's true with quantum fluids like I like called atom fluids.
You can make Boase condensates and so forth and you can get some some quantum effects, interference effects that are completely not in classical Nabby or Stokes. So the experiment that I in some experiments that you may do can be described by Binaggio Stokes. But are there others, some effects which actually had a picture of a globular cluster in the same picture, in the same slide? I don't think the audience can see the question. Oh, so. So the question now.
So Jonathan Holmes asks, what stars in the lobby lacklustre B in hydrodynamic equilibrium and at the end. Are you okay? I don't how I raised it. Unfortunate, but it was on the same slide as the as the one of the Andromeda Galaxy. I had the picture of the globular cluster M fifty four making it so globular clusters that they're much smaller than galaxies,
about a million times fewer, fewer stars. But they, they do seem to be that the stars have crashed into each other enough that they seem to be close to a maximal bowsman distribution and thermodynamic equilibrium. So most Labriola clusters do fit the magnetic equilibrium description and you can use these three fanatic's and hydrodynamics.
Describe them now. When when we gave these practise talks, James Behney corrected me, saying, well, it's not quite there in nomics because the stars at the very tail of the natural bozman distribution is always cut off because there's going to be a few stars that just escape the cluster altogether and fly off to infinity. So it's not exactly natural. Boltzmann, but it's it can get pretty close to Maxwell Boltzmann in globular clusters.
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. One question that I'm so glad to give it. How about the hydrogen that makes it gravitational waves? You know, if anyone's. Oh, boy, that's that's a really good question. I don't know the answer. I'd be surprised people haven't thought about this. I don't know who would be the people to to think about it.
I mean, the thing is that that I'm going to take a guess here that the. You know, the good for most of our universe, the universe is pretty flat. 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. Now, if if the ripples get get fairly substantial, then they can start bumping into each other and and interacting with each other and bouncing off of each other ice.
And I'm sure the people who studied black holes and and more violent gravitational phenomena. I have thought about how gravitational waves interact with each other and whether they form a hyphenated side. I don't know the answer as to how heavy lambrix it gets and whether there's any regime. 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. It it it's it would be appropriate.
I would I would think it's just because there's not enough interaction between the gravitational waves with other gravity of graviton. 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. But I don't know who who's done it. Right. We should stop there, Steve. I think because OK, time, I'm sure you'll answer the questions by typing.
OK. How could you say I stick? Because what happened last time is that I don't much. Russia started answering the questions. All the speakers because he was getting through the list. Oh, OK. So I'll just do this with this one more. I'll get this one by typing Allah. So thank you very, very much for your. My pleasure.