 Okay. Okay, thank you very much. Thank you very much for having me. Okay, so I'm going to talk about something that is it's the mixture of experiments and simulations. A lot of it is in simulations because that's a big better way of having a lot of statistics. And basically, it's a system that looks a little bit like the one in the in the first slide, where we have small particles of colloidal particles that interact. And they are confined between two glass slides. And they're very, very tightly confined. So this confinement is very narrow. It's a very narrow sleeper. And the idea which I am eventually hoping to arrive to is that we can see something that looks like this, where we didn't have we call this be the bidirectional current. So it's a current in which particles on the top go down. And particles on the bottom of the slide go up. So the particles that are white that have a white central spot, they are a little bit above the focal point and the black particles are a little bit below the focal point. So this is like a buckled state. And so the question is, you know, first of all, why are we doing this? And there is many answers, which are some of them are standard, some of them are not so much. The first reason is because what we want to have some way of transporting and controlling transport at the microscope. So this is a very, very old story. Well, not very old, but very popular story in the last few years. It's very difficult to move things in the microscale in viscous suspensions because of what is called the scallop theorem. So the idea is that something cannot move forward by having a reciprocal motion, like the one over the scallop, if you open and then you move in one direction. And then when you close, you move in the in the opposite direction. So a scallop would just do something like back and forward motion. So you need more degrees of freedom. And there's many different ways of overcoming this. One version is if you have a slide, then covers a wall, a hard wall and interface, then you can have some rotational motion and the interaction with the wall will move your particles. And for example, you can have particles that aggregate in little worms that walk. And if you have more of these rollers, then you start having some collective motion. That's one way. Another way is having things that have more than one degree of freedom. This is what bacteria do. So they have, they have flagella which rotate and these flagella are flexible structures. And there is like even cases in which you can minimize or you can have like the smallest amount of degrees of freedom which are two. And this is the Purcell swimming. So it's just simply a couple of hinges. And it's the minimal version of the flagella. Other ways are, for example, to create gradients around particles, which can be temperature gradients or chemical gradients or things like this. And this also moves particles around. So this is one of the motivations. Now, we want to find ways of doing better or better ways of controlling transport in the microscale. The other version or the other reasons that we are studying this is because we want, we know that colloids or in general structures but in our case colloids behave weird when they're confined. There is many different, you know, there is a trivial version of confinement where you go from something that is one-dimensional or two-dimensions or three-dimensions and this changes your the properties of your phase transitions or whatever you are finding, whatever is produced by the specific interactions in your system. But there's also the points in which boundaries, so all the ideas of you know, phase transitions and these things are generally understood in systems with infinite boundaries. And of course, if you have something which is one-dimensional is very well defined and two-dimensional is very well defined as long as boundaries are infinite. But then if you start having something which has finite boundaries, you need to think of how things arrange and how things interact with these boundaries. And one thing that happens, for example, if you do a very, very, very tight confinement similar to what we have is you can get this kind of icing-like behavior into dimensions where particles go up and particles go down. So this is like a triangular icing antiferromagnet. But of course, you have certain restrictions here which break this thing, this frustration that you should expect in the icing antiferromagnet. And another also, or for example, if you start bringing these things out of equilibrium by shearing, the arrangement of particles will change from the equilibrium configuration, which would be something like a hexagonal lattice or maybe a layer of hexagonal lattices to become something that can transverse the directions of the product that something where planes can slide more easily. So this is what happens here, no? And finally, the last reason for this is because we want to have better models of non-equilibrium phase transitions. Non-equilibrium phase transitions, it's something that is so kind of recently or maybe not so studied where the whole framework of equilibrium phase transitions is being tried, we're trying to apply it to non-equilibrium, to systems that are in energy and out of equilibrium, whether because their particles are active or whether they are driven in a random way or in a specific direction or things like this. And it is an open question, how much of these ideas of equilibrium statistical physics can be brought to non-equilibrium without any problems? One of the first ones that are very difficult to bring is the free energy. It's difficult to define a free energy where you have when you have energy coming into the system all the time. And so this is the basics of phase transition is that you look for discontinuities in the free energy. So if you don't have free energy, you have to start looking at discontinuities elsewhere. So this is another reason that we are doing this. But first of all, so ones that, you know, there's all these things that different cloud of topics that these things touch on, but maybe one thing that first has to be settled is exactly what is this thing. So as I mentioned before, we have colloids, which are confined in a very small structure, in a very small slide, sleep board, which is created just by, you know, placing a small droplet of particles and then pressing on top of one, pressing both two cover glasses together and putting a little bit of silicon around. And the idea here is that these two particles are, first of all, they are super paramagnetic. So they have iron oxide domains embedded in a polymer matrix. And also they interact through this dipole moment and also through, you know, heart shell like interactions. And this sleep board is always of a thickness that I don't it's always of a thickness that is between the diameter of a particle and two diameters of a particle. So the important restriction here is that two particles can never be on top of each other and much less three particles. And but of course, a particle has to fit inside. So this is, there has to be a there's many different behaviors that come between in this range of separation of interwall separation. And of course, these are, you know, colloid dispersing water. So there's nothing weird in the substrate or in the medium or anything. And finally, to take advantage of these iron oxide domains, these particles have no moment on the absence of any external field because they are super paramagnetic. But as long as as soon as we apply a magnetic field, then we have a dipole moment. And this this dipole moment is normally thought of as simply being proportional to the external field through susceptibility, which is specific of whatever batch of particles we are using. And you can think of this. So the effect of moving of this susceptibility in two ways. Normally, like the simplest scenario is where our susceptibility is a real number. So this means that if we start rotating the field, the dipole moment will rotate exactly in the same direction. And many different effects come from actually treating the susceptibility as really a complex number in which if we start rotating the field, there's always a small delay between the dipole moment and the the magnetic particle. And this is actually important because for example, these rollers that I was talking about before, if you don't think about this susceptibility, you really shouldn't be able to roll a particle to a magnetic field because you're only rolling the magnetic moment. So this is something that exists. But in our case, we're not going to think about it. Everything that we do from now on in this talk is thinking of a real susceptibility. So exactly what happens between two particles that are that have a dipole moment in under a magnetic field? First, if you just have two particles and you apply a magnetic field, they become repulsive. Now, if you have two dipole moments here, this is the interaction and the interaction is this term dominates and then so you have something that is a repulsive interaction. Actually, this term goes to zero, I think. And as soon as you so yeah, so this is the repulsive part. This is the repulsive term. If you rotate the particles so that you arrange them in a head to tail configuration, then they become attractive. It's exactly like having two magnets, one in front of the other. And then what happens and then there is a point in which so there's a specific angle in which you go from a repulsive to an attractive interaction. This is called the magic angle and it's equals to 54.7 degrees. And then the something that is important is what happens if you start rotating the particles and then you because then you have something that is attractive in one part of the cycle and it's repulsive in one part of the cycle. But it turns out that if you do it very fast, then you can have this thing that is called the time average limit. And then if you integrate the interaction along the whole period, you get something that is attractive. But if instead of just rotating the particles, you add a constant component so you rotate in the plane, you apply a field that looks like this, you rotate in the plane, but you add a constant component in this vertical direction, then you have the pen then the your interaction will depend on the angle theta of this cone. So basically this means that if you are in the vertical direction, you have the first case in which you have just two diapers that are repulsive and you if you are in the horizontal case, then you are something attractive. And again, you recover the magic angle. There is a point in which the interactions is neither attractive nor repulsive. And now the other part that is important to kind of understanding this system is what happens with the confiner or what is the role exactly of these two walls that we are using. So if we just put a lot of particles in a glass slide, you will have just you know, are normal particles. They are, since they have iron oxide domains, normally polystyrene particles have a very similar density to water, but in this case, they are iron oxide embedded in the polymer matrix. So you will have, so they are a lot heavier than waters, they sediment quite quickly. So if you don't have any interactions, particles would just sediment to the bottom of the slide of the chamber. And of course, if you introduce the interaction, particles will become repulsive. Of course, they could, as I mentioned before, if there was no wall in top, they could just come one in top of the other. But this is not what happens most of the case, because as soon as they are a little bit separate, it's just easier to become more separated instead of just jumping one or becoming clustered. But then if you start having a lot of particles, so imagine you have an infinite chain of particles, then you cannot just become more separated, because if chain is infinite, you would have to create densities, higher densities somewhere in the sample. Instead, what happens is that some particles start moving upwards in the cell. So this is what's called a buckled state. Some particles are below, some particles above, and it's the system's way of maximizing the distance between these repulsive dipoles. And so there's some people who studied this and observed that if you have, so you have this repulsive term that comes from the dipolar interaction, and then you have this, this heart increase, which is what happens when particles start becoming, touching each other. But of course, depending on what the height is, you can also get this kind of big dip in the energy, in the interaction energy, which means that if the particles are high enough, you will have, they will be stabling in a dimer configuration or having particles in this kind of diagonal configuration, because you are above the magic angle. So there was some people who studied this in equilibrium, just, you know, they just had some particles in these cells, and they started applying a field, and you see that depending on the number of particles, how dense the system is, you can have something that looks, you know, like these repulsive states. Particles can start arranging in strange configurations, like the square configuration, where maybe you have some particles up and some particles down. In this case, they couldn't see the particles or not very clearly the difference between up and down. And then at some point, particles start coalescing into clusters, because you have these, because it's much safer for them to be close to each other. And then the clusters grow even more until they form kind of this worm-like structures, and then they become connected. So they form these labyrinth-like structures, and then eventually just like a dense system of up and down particles. This is all in equilibrium. What we did is that we wanted to see what happens if this system is brought out of equilibrium. So we started applying, instead of just a vertical field, we started applying this conical field that I was showing before at different frequencies. So before the most extreme cases, if you are going to very high frequencies, then you will have something that is kind of a time average interaction. But below, very much below, you will have first some dimers forming. So pairs of particles, these clusters become much smaller. They change like clusters of their previous slide. They are a lot smaller. They are just dimers, and they start rotating. And they are smaller because they are rotating. It's much more difficult to make a whole chain rotate and to make just two particles rotate. And between these clusters, there's space. So they form these kind of lattices of dimers that start rotating. And as very low frequencies, they are normally almost always rotating in a synchronous way. Like a synchronous way means that they are rotating at the same frequency of the field, of the external magnetic field. Then at some point, these dimers that are synchronous start rotating either in an asynchronous way, which is just something that they still rotate, but not exactly at the same frequency as an external field. Or they just break. Since the time average interaction is repulsive, they just become a glassy disordered state of particles in these popular states of up and down. And then the most interesting for us is the exchange phase. So in the exchange phase, the particles are neither synchronous nor asynchronous. So they are partly asynchronous. But then when they become asynchronous, they break the dimers. And then these breakage of the dimers, they join to other dimers. So this is something that is not necessarily collective because you need the presence of particles around for particles to join to another dimmer. And it's also this intermediate state, which allows particles to not be completely asynchronous and not be completely synchronous, which allows, which makes them break. So I'll talk a bit more about why that happens in a bit. But first of all, is so we drew all these kind of phase diagram of where you have. So instead of this is not exactly a phase diagram is more of a kind of a path diagram. So you have something that goes from synchronous to a synchronous. It's all these orange points. And then something that goes from exchange from synchronous to exchange to asynchronous. And this is the red point. And something that goes from synchronous to to rupture or which passes from through the middle exchange phase. And we can characterize this using some sort of, you know, some sort of order parameter, which in this case, for example, is the relative frequency of rotation of the dimers or the distance, the average distance between pairs of particles. Those tells us information about whether the system is in an exchange state, like in this case, or in a sea in a rupture phase or different states. Sorry, Antonio, I have a question. So can you repeat what is the protocol? So do you have a rotating field that is rotating? It's homogeneous in time. So you're doing a rotation continuously or the protocol is not steady state? For the one? So the protocol is stationary state. So you are rotating. Okay, okay. I just wanted out of the protocol. But then the phases are changing in time. So you have a rotation and then you have a system that is changing from synchronous to exchange to asynchronous. Well, no, I mean, so the change from synchronous to asynchronous, of course, when you increase the frequency. Okay, so you're changing the frequency in your experiment. So this phase diagram, that's why it's not exactly a phase diagram. It's more like a path diagram. It would be like a phase diagram. If you put, if you pull it out of the page and you have a frequency going in, then you have this cube of phases. Here we try to capture the third part where systems, I mean, the phases are these three, four, sorry, but the way that it transverses the phases, it's related to this height and the packing fraction. Okay, okay, I see. Okay, thank you. No, no, thank you. All right, so we did this, we characterized the whole structure of phases and now we wanted to know exactly why these things happen. And the idea here is basically, okay, so if you have something, if you have these dimers, they both have a dipole moment and then you have a relative angle between the dipole moments. So again, as before, if this angle is greater than pi minus the magic angle, then the interaction will always be repulsive. You won't even find dimmers and this is controlled, of course, by the height, by the thickness of the layer. If the interaction, if the angle is less than the pi minus the magic angles, sometimes you have dimers. So this is the first part. Now, sometimes you don't have any possibility of forming dimers, then that's a less interesting case for us. Sometimes you can form dimers, but it depends because if you start going very fast, then you have to think not of what the dipole moments are, but what the time average interaction is, or maybe you don't reach this time average state. The second part is what happens when you start rotating the field. So a way of doing this is to do it very slowly in our minds or in our paper. And here what we do is, okay, so if we have something that is in the plane, then we have two particles and they just go arranged in this way. In a head-to-tail configuration, this is what would be expected of two magnets. We start moving very slowly the field, then our field of our magnetic moments move, but of course this is no longer in a head-to-tail configuration, so our particles will have to move as well. But this motion has a drag, so it has friction with the fluid, so you have to think about the drag of these dimers rotating. So you have two components. We have a magnetic torque and a viscous torque. So at very low frequencies, normally the magnetic torque is high enough that particles can just move with the field, but the viscous torque will always push them a little bit behind. There will be a small phase lag between these two, but of course if the particles are pulled a little bit behind, then just the torque becomes bigger and so they think holding balances out and you have synchronous rotations. So here what we're plotting is the velocity of the angular velocity, the frequency of rotation of the dimers as a function of the frequency of rotation of the field. So this is just, well no, sorry, the relative frequency. This is just one because the dimers are rotating at the same rate. But then at some point, this phase lag becomes too big and so the magnetic torque can no longer grow in the same way because the magnetic torque is something periodic. If you start rotating the dimer around a fixed magnetic field, you fulfill a magnetic torque which is no longer, is not always pushing forward the particle. So as long as soon as the magnetic torque can no longer be greater than the viscous torque, then you start, you have a big dip. So this is the loss of synchronicity and this actually follows very closely an Adler equation which is what you expect from loss of synchronicity things in general. And this point we call the critical frequency and it's something that is very interesting is that it's exactly the same critical frequency whether the other side breaks. So if you have dimers that at some point stop being synchronous and then become ruptured. This is the same, this is a critical frequency and if you, if they instead of becoming ruptured they just become a synchronous, this is the same in critical frequency. So they both come from the same expression which is this dotted line. This is an analytic expression for the instability of this balance of torques. And then it's the same curve. So there's solid curves in simulations of many, many different particles which are co-dating in pairs and also in experiments. So this is, this feed very well to the analytic expression. And then, and so this is kind of explains where do these two phases come from. So the synchronous comes from the two particles following the field. The asynchronous comes from simply particles not following the field but not becoming repulsive. So instead of that they just, in fact if you, so they just sometimes come back or sometimes they follow a little bit longer but then they can come back at some point or maybe they just go slower but then the field catches up with them. So many different things can happen to a single dimmer in the asynchronous. And then the rupture just comes from the time average becoming repulsive. So this is just something that is regulated by the height. But then there's this case. So if the frequency is in this intermediate state you have these states where this goes very, very fast and I'll show it more slowly in a moment. But basically particles cannot be either synchronous or asynchronous. So instead of break, so when they break they don't go into this kind of separated state. Instead they just break and they form a dimmer with someone else. This change is kind of random and it's very nice because they form these kind of learning patterns of where particles are moving. But eventually what we were seeing was this and this was kind of a mystery. We didn't know, so we started looking at this and then the first, so we didn't really know why was the symmetry being broken. So this system is symmetric and so here the motion is random. It goes in any direction and the rotation of the field is also random. Sorry, it's also centered. So it's rotationally invariant. There shouldn't be anything that makes currents in one direction or the other. But we were seeing something that had a specific direction and so we were puzzled. So here the white particles are moving upwards. It's not so easy for me to understand this media. So let's see. You say there is a current upwards of the white particles. So I cannot put frame by frame, I think. But yeah, basically the idea is the white particles are moving in this direction upwards, sorry, no downwards, no? I think. So I see them going downwards. I see, I see, yes. Yeah, so I have a version that is lower later. So but yeah, the idea is white particles are going downwards and black particles are going upwards. Okay, okay. But in the end what is important is not for right now is that they are at least not random. So this has a preferential direction of motion. Yes. So we did simulations, first of all, to try to understand exactly why did we see this. We wanted, for example, to see if we restart the system many times, does this direction change or does it remain the same and things like this? So our simulation as our prince standard, so they're just a brown and dynamic integrator. We have interactions with our dipolar particle-particle interactions mixed with a WCA potential to kind of model these hard interactions between particles. And also they are interaction into a WCA with the walls. So these are all kind of hard like potentials. And then we include this interaction for some gravity because we were thinking about the difference in the population of particles up or down. And then some Gaussian noise because the system has temperature. So this pretty standard stuff. And this part where the particles are moving random, it could be captured pretty well by the simulations that we have. This was no problem. Now here you see they have these kind of small exchanges, small rotations between themselves and at some point they coupled to some neighbors. But we couldn't find why the system was having these directions. So eventually we were looking at the setup, at the experimental setup, and we noticed that in our setup the microscope moves relative to the sample. So the sample is placed on top of the coil. So of course the coil has a big field that goes in the center or has a vertical field in the center. So here this is the coil that generates the constant field in the vertical direction. In our case we would have four more coils in the horizontal directions which are the ones that are rotating. But the problem here was with the vertical coil. So basically what we do is we place our sample, we move our microscope until we find some within where particles are moving or they're not stuck to the glass. There's no trash or you know things like this. But of course when moving the microscope we see that our magnetic field lines are no longer vertical. When they come out of the coils they start diverging and since this is not in the center so they will have this in-plane component. So this basically allowed us to kind of come up with this shape for the magnetic field which consisted on simply applying a constant component to the constant part of the field so that we have kind of this shifted cone. And once we apply this shifted cone we get exactly the same result of these directional currents. And now we have to think about why exactly this in-plane component breaks. I mean it's kind of obvious that it breaks the symmetry but now we have to think about why does it generate currents. And so basically the idea, this is the slower video I was talking about, is we have half a rotation or a fraction of a rotation and then the dimers break but they break at the exact same point where they can join another cone. And this happens both in experiments and in simulations. And here the idea is that this here is the relative angle between the particles, the dimer and the field. And so basically the force that the particles, the interaction force between them it's attractive until a point in which it becomes repulsive and then they just break and go out. This has to do with the point in which the field between the particles and the space between the vector that connects two particles and the field crosses the point in which it becomes, I think this is pi half. So it becomes 90 degrees. So the idea is here this. If you have a rotation that goes as a constant, you know, if you move through a circle at a constant velocity then you're, you know, you feel that goes in the direction from zero to the constant velocity rotation is faster at some points. So this is faster here than here because, you know, here you have a lot of the tangent is further away, things like this. So this is basically what we see when we plot the angular velocity of this vector that goes from here to here. Even though the circular is being traveled at a constant velocity, the point is here is that at some point in this change in angular velocity, it becomes large enough that your viscous force or, you know, your viscous force is growing with the angular velocity. And so the viscous force becomes larger than the torque, even if it's not larger than the torque in the whole system. So the system is synchronous at some points and then non-synchronous at some other points. So this this happened before in the exchange as well. It's the particles don't have a rotation and then break. But in this case, since the this curve makes them break all in the same direction, the fact that they break in the same directions mean they can rejoin in the same direction. And this defines a direction. And in fact, we made a little model of it as before we defined kind of an order parameter in which we can measure this current that goes in this bidirectional current. And we see that this bidirectional current is normalized so that we have a value of one. When all particles are moving, this assumes that the particles are in a lattice, but in the end, they are not in a lattice, but it moves very similar as if it were. And they're moving kind of like half a lattice side every cycle. So this this is what creates a current of one. And here we're plotting a color map where we plot the current. So the blue points is the places where the current is almost one or one. And the white points is the places where we don't have current. So at very, very low frequencies or low fields, sorry, low fields of the cone, we have no current. And then at some point, there's an onset. And this is captured very well by this model of looking at when the system, the dimmer breaks. So this is just something very simple because it's a very single dimmer model. So we're only looking at what happens with a single bit of particles. But of course, this is not a single, sorry, this is not entirely explainable by a single dimmer model because the whole process consists on these kind of particles joining the next neighbor. So it's kind of inedently collective. In fact, if you are a very low packing fraction, as in this case, you will never see these currents, even though you have a tilt. And you will never see them because as soon as the particles break, they just become the hexagonal lattice of ordered particles. However, if you start increasing the packing fraction, you get, again, we get our current back. And then as soon as you, if you start increasing the number of particles, you will see that at some point you start jamming these currents. So you start, then dimmers cannot longer rotate a full cycle because they will hit something else that is in the middle. And they break a lot sooner. So then it's like, if you were increasing the kind of the field viscosity because you have a lot of colors lying around, then at some point, they just create cages and dimmers stop breaking. And so this is what happens around this point. You cannot longer get any current, not because, but now it's because the system is so dense that you cannot not even get a full rotation or half a rotation. And this is actually something we saw in experiments as well. So in experiments, you see a little bit of unbalance between particles that are up and particles that are down because we have gravity. But you get these cages and particles rotating very fast around these cages. And then you don't see any currents at all or any motion. Okay, so I don't know how am I with time. I think I have a little bit of time. You have time. Yeah, no more. All right. So I'll just, this is something very preliminary. This is kind of what we are doing now. And it's not working all the time. But the idea here is what I was saying before about having models of phase transitions. So we have something that sometimes behaves like this. This is a synchronous state. And then sometimes behave like this where you have this exchange state. And in the middle, there is a transition. And we want to understand exactly what is the nature of this transition. So first of all, what we did is characterize this transition in some way. So what we're looking at here is something that is kind of, we call this active because particles are moving around all the time. Actually, I didn't include it, but when you measure the mean square displacement, it becomes diffusive. Whereas in this case, it's always super diffusive. So this is something that is caged. It's kind of in a glassy, disordered state. And particles are moving around these in circles, but these dimers, if you plot the center of mass, they will, it's like an arrested state. So we characterize this by plot, by defining kind of a very weird way of the activity, but it's the only way that we can get around the fact that these particles are moving, they're actually moving, but not, the dimers are not moving. So instead of plotting the center of models of the dimers, which will be ill defined here, because you don't have always dimer, we plot what we call the Voronoi definition of activity. So basically we define a Voronoi desolation of all the positions where the particles are. And then we plot their position one cycle afterwards. So after a cycle of pi house, the rotation of two pi surface. And if our particles are outside of their original Voronoi cell, then we call them active. So this is what happens with all these orange particles, they are active. If they are inside, then it's passive. So we become them as passive. And if we do that, we see that we get kind of this, this very nice plot where we have an activity that is very, very close to zero up until a critical point here. And then they become, the system starts becoming active. And very interestingly, this point, it's a lot sooner, well, you know, a lot in terms of phase transitions, it's half a hertz. It's about half a hertz before what you would get for a single deeper. So the whole system starts breaking not on because there is kind of a field of particles and the mechanism how this happens is still a bit of a debate among ourselves. And of course, all this has to be taken a little bit with a grain of salt because as you see here in many of their cases, we are struggling with something which is we don't always get to the steady state. So this is something we're struggling with, especially because in a lot of these cases, so these are long simulation, longish simulations. But if the system comes to an arrested state, it's very difficult for us to run the simulations long enough that it will become steady. And most of the times it comes to something that is an arrested state. And this is, I will not discuss this, but we thought of some strategies which some work some own. But the idea here is, is this an absorbing state? Because this curve actually looks a lot like curves of absorbing states. So you have something that is flat here, something that becomes active here. And this is very similar to the, you know, these things where you have what you see in emulsions. You have shared emulsions. Then at some point, you have something that looks similar to this curve. But first, so what is exactly an absorbing state? To be brief, an absorbing state is what you expect from, for example, epidemics. So if you have a population, then you have someone who is infected. And then you have a lot of people who are susceptible to this infection. And then, you know, if you start progressing in time, then some more people get infected. Then more people get infected. But you know, there may be these two recovered. And so eventually you come to a steady state, which might be something like, you know, there's a bunch of people who were infected and recovered, but now have immunity, but all these people have not recovered, have not been infected, or maybe you have everyone infected. Now, these two are absorbing phases, because once the infection died, whether because everyone got sick, or because, you know, most people who got sick got better without infecting anyone else, then it's theoretically impossible that you will get a new infection. Of course, now we know that there are fluctuations, and that's the reason we are in the situation we are now in. But so the idea, you know, in the absence of fluctuations, this would never come out of this phase. And so the idea here is to see whether or not these, so if we start rotating our demons, this just rotates in its place very fast. So this video is very fast. But if instead of that, we start a little bit after the critical frequency, or maybe very close, then we would expect the system to start creating places in which the system is active. And of course, these places should activate other places. Now this is something that if you look at this video, it doesn't really seem like it's an absorbing state, because there is some, there is many places where the activities is coming up. So this is something that we have to think about whether, I mean, there's nothing in the model of active of absorbing phases, which says that it has to be locally generated. So it could very well be that it's just an active state, but it's generated through long range modes or something like this, or simply it's not something active and it's something else. So this is something that we're working on now. And so, you know, to summarize, we saw these colloidal currents that I talked very much about, which are produced by this breakage of symmetry. And it's very interesting as a transport mechanism, because it doesn't require, so you know, you have this driving from the outside, which is kind of, but it's an isotropic driving. You don't have to pull particles from any direction. It's kind of this collective motion where particles are grabbing onto each other and pulling themselves forward or backwards. So it doesn't, it requires a little more than this paramagnetic dipole and some sort of viscosity, you know. And the system has these non-equilibrium transitions and we're in the process of trying to understand exactly what is the nature of this transition. So I think that's it. Thank you. And thanks to all the people who were involved in this, all the things that I presented and thank you for listening. Thanks a lot, Antonio. I give you a virtual clap from here in the name of everyone. And so there's some time for questions. So please, anyone see someone with the camera? Nicola maybe has a question? Okay, fine. So I have a question related to the current. When you plot the current as a function of time which reaches a stationary value. I don't know if you can go back to this. This plot is very interesting to me because when you plot on the right, it's the average of this fluctuating value. What you are plotting in the face. Okay. But did you look at the variants of this current and the fluctuations? No, we didn't. But now that you think you mentioned it and thinking about after looking at all these things about phase transitions, it makes sense that maybe we should have to see if there were spikes. I don't know if this is where you're going to but to see if there were big increases in the fluctuations around the phase transition. Yeah, no, we didn't. This is something that maybe we should have. I'm telling you because there is a lot of research on this topic in stochastic dynamics now because systems that have very precise currents, meaning that the variance compared to the mean is very large, are associated with dissipation of heat. So systems which are precise have a cost which is in this case would be, for example, the collides are moving very quite deterministically with a given current and this as a cost which it would be the dissipation of heat in the fluid. There are many results relating to this and maybe something could be done along these lines for the model because you have a land-driven model so you have a viscosity, you have heat dissipation in the model. You have currents and I think this is data you have there and you could use it for further studies. You could take a look because I'm sure you will have a big heterogeneity of variance in the current in this phase diagram as you show. So here the point would be that the current should have a very small variance but then the particles should have large fluctuations around there. I think that when you have a very ordered current this means that the particles are going almost like straight lines but they are also because of this they dissipate a lot of heat in the bath. So more precision would imply more dissipation and this is... It's a bit interesting. Yes, I think we could discuss more in detail. Because your model is a land-driven model with non-conservative forces so there is dissipation. It's not just a potential, it's just you also have a driving out of equilibrium. Yes, I think this is something we should think about or I should think about and maybe... Yes, we could discuss. I think it's a great system. Very good. Okay, other questions? Okay, maybe last question about the experiment. Can you comment on what is the material they use in the experiment and what is the main challenge? Because I imagine that the particles can be stuck to the to the glass surface. Yeah, that's always something that happens with colloids but no. Okay, so we're using... This is polystyrene and they are magnetic so they are these commercial polystyrene particles that you buy that are magnetic. They're actually used for immunosides so you basically move them around your sample with a magnet in biological labs. We of course do something completely different from what they are meant to but the main main challenge really is having a control height actually and this is something we've been working on on and off by you know having you see because these are you done as I told you like we put a droplet with press they're actually they're cover slips so they're very thin and then at some point we seal the sample and actually what we do have is we have many different regions because the one of the cover slips is usually not completely flat. So this means that we have many different regions and one thing that we're doing now is we're trying to do this with microfluidics basically with having some pvms on a thicker glass which is normally very homogenous and then you can have something which is much more controlled. So the biggest challenge is having well controlled heights for long distances. I think it's quite challenging. Yeah. All right so any other questions? I've seen no questions so okay so let's thank again Antonio for the nice talk and thank you for the invitation. So I think we have