So thank you very much for coming, everybody. It's very nice to be able to talk to you, too.
Robbins told you about active matter.
My first couple of slides are just perhaps really summarising what he says.
And then I'm going to talk about two particular problems that we've been working on,
perhaps more the background of the problems than what we're actually doing.
One is how do bacteria swim and why is it different from the way in which people swim?
And then the second one really is the research we're doing at the moment,
which is we think topological defects might be important in how this whole how the collected motion of these active systems work.
And so I'll try and explain at least the background to what's going on that.
So Roman told us a lot about the cells.
These are molecular motors, which are the engines which drive the cells of bacteria, even perhaps flocks of birds and fish.
What these systems all have in common is that these active systems,
they operate out of thermodynamic equilibrium all the time, this energy being pumped in.
Most of them are living systems because living systems have to be out of thermal equilibrium to live, otherwise they're dead.
It's really very bad. But sometimes you could imagine other systems like, for example, vibrating, granuloma,
or if you have a ledge grains and you vibrate them up and down, then you're pumping in energy all the time.
And our questions are, what's the same and what's different about all these different systems?
We know lots of things that are going on in these systems. We don't have a nice theoretical physics, generic picture of what's going on.
Maybe we can't. Maybe it's too complicated. But I think there are signs that there are, at least in some of the things that are going on.
Useful things that physicists can say. So why are we interested in active matter?
Well, this picture is really a way of showing movie.
Movie. Yeah. Okay.
This is the thing that Roman was talking about. This is a large collection of bacteria, and you can see this swirling around like this.
And I'll come back to that in more detail later. We've got a lot of active entities working together.
Statistical physics, which you learned about when you were undergraduates.
Tells us what happens if you have loads of things together. We know that in equilibrium things come as described by the Boltzmann distribution.
We understand the velocity distribution of these systems.
We've known for a hundred years how to cope with systems in equilibrium.
Here, we know nothing in equilibrium.
Is there a generic velocity distribution? Why? When you put these bacteria together, do they swirl around like that?
So there's some really nice physics questions about non-equilibrium statistical physics, but also these things are useful.
They really are going to be useful as microscale engines.
And this is a lovely little picture from the Rover Group.
What this is, is a tiny flywheel, about 50 microns across, about a 10th of a human hair across.
And it's embedded in a load of fluid or a load of bacteria are swimming around.
And again, it decides to move and it takes a while to load those bacteria pushing that flywheel around.
That was just a gas. It wouldn't work. It's because the bacteria are an active non-equilibrium system that it is moving around.
And so what we've got here is a little machine where you're translating chemical energy into mechanical energy.
And I think that's going to be the sort of idea is going to become increasingly important maybe in ten or 20 years time.
So why? Why now? Why is active matter interesting now? I think it's really because of better nanotechnology and better microscopy.
So people can do the experiments.
They can build things like that little fly wheel, and they can actually look at the past of the bacteria moving around.
From our point of view, faster computers have made a big difference because we can simulate these systems and then we
can look at our models and see if they actually work relative to relative to the real systems.
So the first question I'm going to ask is how do bacteria swim?
Then I've got bacteria which are much less dense in the system. We have so far these little swimmers swimming around.
And let's think of them just as independent of each other necessarily.
And yet these ones, like these ones are basically they could be carried out.
And so what's going on? Well, first of all, they're living.
So there might be all sorts of nasty conflict complications due to that.
They might be hungry or not like each other or something, something like that.
We can forget about that. They're tiny.
They're maybe 1 to 10 microns. So thermal fluctuations are going to play some role, and we're going to forget about that for now.
And then the third thing is that they're swimming in a third.
And so what's going to happen is that they're interacting with this swimmers and they're going to set up flow fields in the surrounding fluid.
And that's what I'm going to concentrate on how these things set up flow fills in the fluid and why they actually move in that fluid.
So this is a theoretical physics morning. So that's the equation, right?
Now, this stokes equations describes the notion of a fluid.
B is the velocity, rho is the density, T is time. This is the driving force and gradients of pressure with that.
And so through the field, any applied forces will pick up the flow field.
And then this is the viscosity, this new here is this quantity.
Now the important thing from our point of view about this equation is that two to this point, if you push the fluid, there are two ways it responds.
First of all, the things on the left of the inertial turns and then those on the right is this supposed and the way to think about that is,
is if you're swimming through a swimming pool and you stop moving.
The inertia is the thing which keeps you going, keeps you gliding.
It's how momentum is transferred through the fluid.
And then the best systems are the ones which eventually bring it to a standstill when you stop because momentum has been dissipated in the fluid.
And the Reynolds number is the dimensionless number, which measures the ratio of those terms.
And this is if you bung in numbers, what you find is that the Reynolds number is these three factors multiplied together,
basically because they're so tiny, the length scale is about two micron,
the velocity scale is about a micron per second and growth of the viscosity comes out to six if you go and look it up.
And so the Reynolds number is tiny. The attendance numbers are tiny.
And so you can forget about this side of the equation. And instead of the Nazi sex equation, you have just the sex equations.
And that's what makes sense as well in a very different way from people.
What would happen if you were selling at very low rents number.
Is that everything would seem really discuss it be like like a swimming in
treacle and it would mean that if we stopped moving we would stop instantly.
So these are some things to help with swimming in support.
So the key things that are going to come out of that,
two things which especially if you're selling at low number and the first one is the scallops and lots of scallop does I think for me to do that.
Yes, initially. But right now, that's just expectations. That's an obvious sense without the initial bit.
Now, the thing to notice about this is there's no time dependents in that notice anywhere, no time dependence.
And that means that there's nothing in the equation which makes the difference between forwards and backwards in time.
So this thing is going to have a hope of moving.
There's got to be something in it swimming straight, which tells you the difference between forwards and backwards in time.
And this is what the Skull Theorem says.
The skeleton says that if your microscopic low redness number swimmer,
then your stroke has to look different forwards and backwards in time for you to be able to move.
So a scallop just goes like this. Okay. If you run that backwards in time, you couldn't tell the difference.
So what the scallop would do in a low, Reynolds number fluid is move a bit and then just move back to exactly where it was before.
So how? Just do it. Why?
I mean, this is one reason why that the shape they need some way of swimming which has this time reversal
non invariance in it and the way they do it is by having long flagella or helical tails.
And so when they move a wave moves down here and a wave has a direction to it that's allows them to move.
This one here has a helical tail. And because it's a helix, the helix has a handedness to it.
And that's what allows them to move in a certain direction.
That's how the real world does it, how the theoretical physicists do it.
This is a model that Roman is famous for writing down a while ago now.
This is the sort of theoretical physics version of those swimmers.
And what it is, is three tiny spheres which are held together by rods, which was Edmunds forget about.
And the swimming float is like this. It's left one in, right, one in, left, one out.
Right, one in. Okay. And if you make that thing go fast, it will just about manage to win.
And the reason it sends the asymmetry which allows it to turn is really quite a subtle one.
When this one is moving in, that one is out.
Whereas when this one is moving in, that one is already in gear.
And so when you think of the hydrodynamic interactions between those spheres,
which is what actually makes it move, it's that very small imbalance which actually makes this thing move.
So what it does is it moves forwards and backwards, but not quite as fast.
And so eventually it manages to keep going.
And you can play with these models that one will swim because it's like a wave moving along.
And then in two dimensions, this one here, this is the Oxford rower.
And that moves like this. And then this one down here, which has arms of different lengths.
What that one will do is move in two dimensions. And this one is the Cambridge, rather.
So they don't really look much like real swimmers that they they run the number.
But the reason the reason they're really nice is that we can actually do the math for them.
So you can actually solve these things exactly. And get things like the swimming velocity.
So the next story really is now let's forget about them swimming.
Let's think about the flow field that they generate around themselves.
So now I'm going to ask what does the flow field look like a long way away from this year?
And we actually can find that exactly for one of these spheres, which is why this is sort of a nice model, because we can actually do things to it.
So let's go back to the Stokes equations and let's ask in various degrees of fanciness, what happens when I have a point force acting on that fluid?
Okay. Or if you like it, this off mass of people.
If I've got a colloid and I pull it through the fluid, what does the flow field look like?
So those of you that perhaps made it beyond undergraduates, this is the greatest function of the folks equation in this thing.
It's called a Styx that. The thing to notice is it's the velocity of the long way away.
Is just point force on the fluid. That's the force. That's the viscosity.
And the important dependence isn't the velocity goes this one over all.
So the velocity goes is one over the distance from the swimmer.
Those of you that represent the Greens functions.
This is the picture which says exactly the same thing. I got a little force here, I think maybe on the colloid pulling it through the fluid.
This is what the flow field looks like. And perhaps the most important thing is that the flow feel definitely has a direction to it, as you'd expect.
It actually sort of moves here from that way to that way.
Dex That goes this one. Overall velocity field goes this one over.
Now, remember, remember when you did electromagnetism?
A while ago, perhaps. And if you had a charge, the potential.
Whence is one? Overall, you solve the pluses equation charge.
Okay. Potential guys is one overall away from that charge.
Now, remember, what happens if you now have two charges of plus and minus charge next to each other?
Okay, that's a dipole. And so now the one over four times cancel from the plus and minus charge.
So a long way away instead of one. Overall, what you end up with is a field which goes this one over all squared, a dipolar field.
Now it turns out that the same things happens for these Sunnis.
Because it's swimmers autonomous, you're not putting a force on the swimming themselves.
So when they move, all the forces have to come in equal and opposite paths.
Because by Newton's law, there's no other way they can do it. So for a swimmer, all the forces come in equal and opposite paths.
And indeed, for all these active systems, the forces come in equal and opposite paths.
And so instead of having a flow field, which goes as one overall,
you have to add up two of these flow fields, one from each of the forces on the swimmer, if you like.
And this starts to look a bit like Roman silver, which is why it's a nice model.
We can do it. Exactly.
So you add up the flow field from each of those forces, the leading all the time for that, and you end up with a dipolar flow field.
And as my dipolar flow feels, we know it's dipolar because it goes this one over all squared, just like the plus and minus charge together set.
I always get shouted up by the experts when I say that's not quite the same because these are forces, not scalar charges, but they're enough.
So the swimmers have dipoles across those fields, and that's because they're active systems which produce their own energy and their own force fields.
And it turns out there's quite a lot of cases where that matters.
And the next few things I'm going to talk about places where it matters.
But first of all, let's just look what that looks like.
You get this one overall spread, but you also get an angular dependence on the angular dependence.
Looks like this. This is my swimmer.
It's pumping fluid out from its sides and pulling it in from its ends.
And you can see the symmetry is very different here. The flow is being pushed in that direction.
Here you have a symmetry in the flow field around this line.
And indeed, these swimmers can either either pull the fluid in from the ends and pushing out from the sides,
and that's called a Pollock contractile swimmer. Or they can do the opposite by just change the sign of the dipole,
the direction of the flow field changes and it pushes fluid out from the ends and pulls it in on the sides.
So does it work? No. It's anything to do with reality.
Let's look at some real sinners. And these are some very beautiful experiments from the Goldstein Group in Cambridge.
And this in recent experiments, I mean, this is what I'm saying, that we really are now not many,
but people in general can do these experiments in the last couple of years or so.
This is the flow field around the paralysed. And you can see it's pushing fluid out from the ends and pulling it in from the sides.
That's just this bipolar structure that works. This one here is coming to Main US.
This is the one that does get stuck again close to.
It's a bit of a mess due to these failures. You get these vortices and if you look a long way away,
it's pushing fluid out from the sides and pulling it in from the ends so that ones pull up the pusher and that one's the puller.
So that's right. And that all fits with the picture. So it really works for real systems.
I'd say you get to this one, this wonderful box. And this is a pretty movie, of course, a big one in the minutes of that movie.
And if you look at the posters around Volvo, it looks like this.
Which way is it going? This one here. And that definitely isn't this type of stuff.
So we've got a bit of a problem there. But that actually it's all right is because of all the boxes is fairly heavy.
It's a big spoiler. And so it's got gravity acting on it.
So there is a net force on this. So you're away from this, this balanced fourth story box and things like that.
And back to seeing a flow field which moves like this.
So what we are particularly doing at the moment would talk about that.
Is. Asking if I have seen this like this and this is real.
The real questions we are asking at the moment.
Research for the last couple of years, we have seen this like this how the particles move near the source.
So so this is really the question. This is a nice old box movie.
And you can see here that tracer particles, just bits of dust, basically, which you can throw in the fluid which follows the flow film.
Okay. How do those moves? Can we predict how they move in the background like.
So let's let's just ask oh, I did this one as well because this one's key.
This actually is cheating or that causes too big to be a no one's number seller.
But it's a nice experiment showing how the tumour mixes the fluid around it and there's a big argument in the literature.
There was a lovely nature paper by the first two authors. Do small swimmers mix the ocean?
Because they might be small, but there are a lot of them. And then unfortunately, all the other authors at the paper say, no,
they don't because everything happens on two small land scales to really mix things on a large scale.
But everyone always starts saying it's really a pity that because this is a lovely idea.
Okay. So. So we want to know if I've got a swimmer swimming around.
How does it trace the particle one which just tracks the flow field move near that swimmer?
And so being a theoretical physicist,
the easiest thing to do is have a swimmer which swim quite happily in a straight line and plus infinity to minus infinity.
And that's put in a particle and see how that particle moves.
And the answer is, it does this. Making the.
Closely. We were surprised about that. Okay.
But actually, it's fairly easy to understand why does the close knit, if you remember, about this dipole flow field.
So here's the dipolar flow field by swimmers coming like.
This, but that's a bit hard to see.
So instead of that, let's have the tracer coming like this that sits in the rest of the swimmer and having the tracer move like that.
And you can see that here, the trace is going to be pushed away from the swimmer.
By the time it gets here, the trace is going to be pulled towards the swimmer.
By the time it gets there, it's going to be pushed away from the centre again.
And so everything's nice and symmetric. And so you get pushed away from the swimmer pool towards the swimmer, pushed away from the sun.
And you get these dipolar loops that.
And although that system for what it turns out to be a really nice starting point to ask the questions about when in this loop that goes wrong.
And you can.
I'm not going to go into it now because I'm not going to have time. But the places where the picture goes wrong is, as you can imagine, some mistakes.
And that's been happening in straight lines. But but you can work out what happens if they instead do random walks.
And the other place where it goes wrong is that if the price is placed to the swimmer and its velocity is the same order of the swimmers,
then you get a different behaviour because you do actually get the tracer called along with the swimmer.
But that's details and perhaps perhaps from another more formal talk.
Now, let's just look at this movie. What this movie is, is the the green things I thought.
And the red things are the traces. And so we can actually look and see how these cases are moving in a real system and.
If I stop it at the right moment, which is the tricky to do. You can see here very nicely that you get these looped structures.
One of the some of fluctuations here as well. So, you know, only some of them do the right thing.
These here are doing loops very nicely. Okay.
So you really do see these loops in the system. Here you see something a bit different.
I think there's a swimmer behind that. So let me just stop it a bit further on and we'll see.
Sometimes you get these long trajectories. These here, which are being pulled along by the swimmer.
This is what we call in training. These are places where the loop breaks down because it takes and moves too fast relative to the swimmer.
Those of you that are the experts, you have to include the Negro in hands in the equation.
Okay. So this again, is another example of how people are now being able to do these beautiful experiments.
Now I'm going to swap. Topics.
And I'm going to not take consumers and put lots of them together.
So lots of bacteria together. Okay.
And this is a picture I showed you that like on Roman Shoji, we now have lots of bacteria, collective system.
And what's happening is we're getting these swirly flow fields.
These things are swirling around all over the place. Like turbulence.
Okay. Like the water, maybe at the bottom of a waterfall.
And, um, this is a problem because I'm zero reynolds number and turbulence is meant to be a high Reynolds number phenomenon.
So something is going on that we don't understand and we'd like to be able to understand how to predict this active turbulence.
And what I've done here is just draw a picture which shows the vorticity at that flow field.
That's just a measure of whether it's swirling to the right or swirling to the left.
And the red bits are swirling to the right, and the blue bits are swirling to the left.
And all I'm really doing with this is if I want to use this as a way of representing this field,
to show you that the same thing happens in many different systems.
For example, this is actually a computer simulation. It's a simulation of long road.
And all the roads do is move with some sort of velocity.
And then there's a short range interaction. So they can't penetrate each other.
They just sort of bounce off of each other. If you plot the velocity of the rog if there long and thin enough aspect ratio about 5 to 1.
What's sorry this is the picture. It's the same height, very different system.
We don't have any fluid in here. We just have these rods bouncing around.
So you get the same sort of structure in the velocity field.
These are these migrated grains things. Again, you get the swirling in the velocity field.
Okay. And if you plot shells and fish again, you get this sort of swirly nature of the velocity field.
So then theoretical physicists get interested, right?
Because what we like is when things are generic over lots of different systems, some of these have hydrodynamics, some don't.
I'm a big somersault. How much can we describe what's going on using just the same thing, the same generic feeling for all these different systems?
Now, since we don't know, but this is what we're trying to think about at the moment.
And this is, you know, maybe a beginning. It's an idea.
It's an idea I talk about at conferences. I'm confident enough to do that.
I use it for face it with the I don't know if we're right or not yet.
Okay. So the particular system I'm going to look at is molecular motors.
So now we're back down to the cellular level. This is.
A microtubule, which is parts of the structure of the cell, such as strands like tracks which are found in cells.
And this is a molecular motor, which is just a protein, a motor protein moving along this track.
And this thing here is, in fact, that basically it's a vacuole which is carried around in the cell.
And the first time I saw that, I thought, oh, yes, oh, you can't possibly be like that.
But they are they really are like this. As far as we know, they really are like this.
These are real pictures of a real molecular motor has its front foot nurses back foot.
I won't show you the movie, but there is actually a movie showing it sitting over there.
We see much a very good movie, but there it is in its next position.
Then it moves on to the next position and it does it by the back foot.
So the getting unbound, looking forwards, moving, it seems like it's walking along the tracks.
Why tracks?
Well, the reason for the tracks is that these things are tiny and nanoscale, and so the thermal fluctuations are enormous at these little scales.
So they have to be tied down to gas anyway. So swimmers are okay on their own, but these things do need tracks to walk along.
I'll try and just outline the way it works because it's so amazing.
I mean, I'm not enough of a biologist to really understand it properly, but it's the structure of the proteins which make it work.
What happens is that the back foot gains a molecule of ATP, that's the chemical energy, and that binds it.
That allows it to unbind from its track. Okay, then because of the shape of the protein, it's almost elastic.
It has some sort of chemical elasticity in the ball, which tends to flip it over.
So it's in front of the other foot. And then because it's closer to the front of the track as it diffuses around, it tends to pin down inside.
So these things are only going to be processed on average, but then they're able to move from one place to another.
So it really is protein engineering, which makes this possible.
John, how many going until about quarter two, is that right?
Yeah, that's about right. Okay. Okay. So let me show you this.
Maybe let's just have a bit of time out of the same thing and show you the movie, which comes from.
I can get it to work. Beginning of this. This is from YouTube.
It's called The Inner Life of the Cell. Some of you may have seen it.
We get the fancy sounds as well, and I just like it.
And in particular, let us look out for the major proteins that we see.
What we're seeing here is in a minute. The actin filaments which are the surrounding of the cell.
This is the cell wall. These are the lipids which make up the cell wall.
I hope they're interested in. I got a bit confused.
What's what? After a while? Yeah. There's a text from accident.
Which. Which which acts as a scaffold at the edge of the cell.
Yeah. Now, these guys here, these are the filaments. These are actin filaments, which is one of the parts that some of these motors walk along.
And they're continually being formed and then unformed again.
So this is the scaffold of the cell. And this gives you an idea of how complicated these things are.
Those are proteins which are meant to cut these apart.
These are microtubules, which is another sort of track, the ones that arm later walks along, the microtubules on forming.
And here's our motor coming trotting along. He's a pause in the cell wall through which possibly ions are coming.
These are the things Ramon was showing you. I forgot the name of Go There Apparatus, I think.
There it is again. So I really recommend this is a sort of shortened version of it, but I really recommend if anyone's interested,
it's on YouTube in a life of the Cell, and this is meant to be as close as they can get to to reality.
Well. So.
Right now.
The reason I talked about this is these are the experiments that Robin showed you the movie from where you go through a swirly things going on.
And this is a beautiful set of experiments recently done in a dodgy group at Brandeis.
What they did is take some of those microtubules and take them out of the cell and then put in some molecular mode.
So what you have is microtubules plus molecular motors.
And then the important thing that made our experiments work is they put in this thing called Peg,
and what Peg really does is just push the microtubules together.
So they were able to get a very dense solution of these microtubules.
The microtubules have a directionality to happen when the motor lands on them.
When the motor lands it walks in a certain direction and so it pushes the microtubule in a certain direction.
And so if the motor which attaches in this case with a head on that my head is motor.
So they attach the to microtubules and if they happen by chance to do it so that this one works that way and that Ted walks that way,
the two microtubules move relative to each other.
Okay, so they get pushed apart if they happen to land.
So they're both moving in the same direction. Nothing happens. They just sort of walk down the microtubules and fall off the ends.
And it's this pushing in the two different directions that gives this swirly pattern.
So what you end up with is these these white things and the microtubules and then the yellow arrows and the velocity field.
And again, you getting this swirly sort of velocity field, this turbulent like pattern in this system.
So an active system is giving us this active turbulence.
And the particularly nice thing about this experiment is that they went a bit further than that.
They didn't just say, Oh, we get swirly patterns. They actually measured something.
I mean, this is where we are with this subject.
We're just starting to be able to measure things along with the velocity, velocity, correlation function.
Let me remind you. So it's the correlations between the velocity here and the velocity here.
If this point here has a certain velocity.
What's going to happen is the ones nearby are going to have the same velocity, but that gradually those correlations are gradually going to go away.
And this is the raw data. This is the velocity velocity correlation function as a function of distance,
but different strengths of the activity, different amounts of ATP fuel in the system.
This line here is really the velocity squared. What happens when you're ready?
Very when you're just looking at V0, v0 is the velocity squared.
And so if you put in more fuel, the velocity goes up.
What makes a lot of sense? But then they took this stuff and they plotted it so that all these points were normalised to one.
So they just took the curves and scaled them. So they all started off at one and you can see that they decay away like you'd expect, right?
But then what's weird about these curves is that they all fall on top of each other.
And what that is saying is that you've got to let it scale, which tells you the lengths over which the correlation is decay.
And it's independent of the activity. However many, as you Chuck, in this system, the length scale is independent of the activity.
And the reason that's nice is that you wouldn't expect it.
And so it's a really nice thing to try and explain. You've got some chance of your theory being right, certainly seem relevant if you can explain.
So that's why we like these experiments so much. Actually, we've done the theory first.
We found the same strain, same thing, and then discovered the experiments.
But that wasn't the right way round. Done it? Yes.
Okay. So that's the first thing. That's what we're trying to do now.
The next thing I have to tell you about is liquid crystals. Liquid crystals are long, thin molecules.
And I'm not just talking about ordinary self matter, I'm talking about this is liquid crystals you have in your laptop or maybe in your watch.
The long, thin molecules. And it's high temperatures and low densities.
What you end up with is they just like a liquid.
But if you then go to higher densities or lower temperatures, what happens is these things line up to be all approximately in the same direction.
And you got to think of the maximum. So in a matic you have directional order but no positional order.
It's still a liquid, but it definitely has a direction to it.
And these microtubules, because they're long and thin behave in the same way as in the matic, except the bigger.
And so you're a bigger scale in these molecular systems.
And what's important about this new metric, say, for our purposes, is that the pneumatic phase can have topological defects in it.
Places where the direction of this directive feels so out say that this is the directive field.
This is the direction it wants to go. Yeah, the direction of the microtubules, if you like,
get tied in knots and you get possess places like this where where this is a topological defect
because you can't unwind it by any continuous change in the direction of the microtubules,
if you like. It's like a knot in the director field.
It's a place which you actually can't have in an infinite system because it has infinite energy.
The distortions go on forever. This shape is a minus a half defect.
This shape is a plus a half defect.
And these pictures are pretty pictures of the magic between cross polarisers, where what you can see is these is these defect structures.
Okay. So that's that's our political impact.
So remember that because that's going to come back in a few minutes.
So I talk about the experiments. Now let's talk about what we do, which is simulations of these things.
You write down the continuum equations which are the same as in every six equations,
but for these little crystals plus an extra term which represents this extra energy that the gave because you've got an active system here.
And it turns out that the form of the equations rely on this idea of this dipole again.
Remember we said this a swimmer was a dipole because it has two equal and opposite forces at any time or more than two.
Okay. These are the same, right? These move relative to each other.
What the motives are doing is exerting equal and opposite forces.
So again, equal to dipole. It's an active system. You can't have any net external force.
All forces come in equal and opposite pairs. So it's a dipole.
And based on that symmetry, we can write down the continuum equations and they take up a side or two.
I won't write them down, but we can do the two things that one has to to know about these equations.
First of all, the minute you turn on activity, the pneumatic state is unstable.
So the state of all the microtubules aligns it in the same direction.
If you do a linear stability analysis, it's unstable.
The second one is that if you have this pneumatic and have any gradients, any gradients away from the automatic state, you get a flow flow induced.
So we did the simulations, we sold the equations.
Basically, you saw the equation. We get the same story, same sort of picture.
This active turbulence, active turbulence where you get read between events which corresponds to this velocity field moving in different directions.
And if we zoom in, we can see those two things I've just said.
First of all, here's a nice animatic, but we've turned on the activity and we've had this instability.
It's become unstable and we've got tanks in the direction of the microtubules locally.
So immediately we see while we get this chaotic flow.
What's on the activity director field becomes unstable.
We get kinks in this direction of field. Kinks in the direction of the microtubules.
The minute you have kinks, you introduce a flow field.
Makes the matter even more unstable. Okay, so we've ended up with this active turbulence because the axis makes the pneumatic state unstable.
So that's life. But. So, Alison, why we detected turbulence, but we don't understand anything about its properties.
Is it going to be the same in all these different systems?
Well, let's check if we get the same physics from our simulations that they did in those experiments on microtubules.
Remember, this was the picture I showed you. The length scale was independent of activity.
Did exactly the same experiments, if you like, without any merit.
Calculus is exactly the same thing. And again, velocity increases with activity.
Well, I put everything on the same curve.
Beautiful days to collapse on to the same person.
So the equations and the molecular motors seem to be doing the same thing.
How can we explain what's going on? Well, we're talking that the pistols.
The minute you think about liquid crystals, you think about these topological defects.
And indeed, if you look at the experiments, they've actually found them.
So these are the experiments, these white things, the microtubules.
You can see the direction to them. Here it's looking like a plus or half defect.
Here it's looking like a minus a half. Okay.
So you certainly seen that in the simulations.
We can follow these the effects around. No, they are the same simulations.
But what I'm actually changing, I see psychological defects.
The red ones are plus a half, the blue ones are minus the half.
And you can see them doing what topological defects do, just like plus minus charges.
They annihilate each other. Nothing minus always annihilates each other.
But it's not quite all the story, is it?
Because if you look at that movie again, what we find is that at the end that pretty much the same number of defects as they were at the beginning.
So they're certainly annihilating each other. Let's do that again. I think if you look carefully, I think there's one up here.
They're also being created. That they should be annihilated and created.
And that's a bit new because in loads of systems one sees these defects.
And what happens is the minute they find each other, they destroy each other.
And so eventually they go away. But here that creates it as well in a normal liquid crystal,
if they are created there right next to each other and they immediately are destroyed again.
So you never see them here. Is that created near where they are?
There are all sorts of distortions in the director field. And so the flows created, so they're created and they move away from each other.
And so they manage to get away with not being immediately annihilated.
And that's something really rather new and which we're quite excited about trying to understand this gas's defects.
We actually did a simple theory just based on this idea of defects being created and annihilated.
I won't go through it, but what you do get nicely is a velocity velocity correlation function, which does not depend on activity.
So we end up doing just a simple theory with a length scale, independent of activity.
So this might be an explanation for what's going on seem to fit the data so far.
It works with these experiments on notice as the big questions about whether it works through other systems such as the bacteria.
And I think there are also some nice stories about about some of the spots we have to do,
sort of nice because these technological defects you can find all over the place in physics.
Dislocations in crystals are topologically defects.
Really yet enough people think it's a political defects were important in the formation of the early universe.
Here's some other examples. More labour physics.
But normally these things just want to destroy each other.
And so it's really the case, I think, having a system where that created as well.
That's what we're trying to think about at the moment.
The way in particular is is actually somewhat that we've been able to work on this and unpack for $0.30 Iran.
And this contributed a lot to this. And with that, thank you very much for listening.