 No, it's fine. It looks fine. Where's the mouse? The mouse? Thanks to the organizers for inviting me, for giving me the opportunity here. I will talk about active matter. Basically it is friction, but it is friction between fluid and solid, as we heard this morning, and sometimes also between fluid and fluid. Let me start with a movie, and I hope it will work. This is an island where Impala is trapped, and there is a croc waiting for the Impala and swimming, hunting it. And you see, the croc is faster than the Impala, and I cut the video here, since it's a bitter end. So it matters how fast you can swim, maybe again. So the croc is in the bag, it decides to jump, sometimes there's no other option, but then in the water, I mean, the croc is overtaking and approaching. It sprays. So this happens also in the micro world. This is a micron-sized white blood cell, following the bacterium, which you see, and it now swells it. That's it. That's the end of it. So the conclusion is, the swimming speed matters, and if the swimming speed matters, friction plays a role. If you swim in a superfluid, I don't know how to do this, but it makes a difference than if you swim in honey or in water. And it depends on a lot of things, your shape, but in particular also the propulsion force and also the technique to swim. And this is, I think, a pretty new research field also now in physics, if you go to the micron scale here, and then if you estimate what is the typical number, say the typical Reynolds number, Reynolds number is the ratio between inertial forces and viscous forces. Then viscous forces, you are in a viscous liquid, are very, very large relative to inertial forces, and this has to do not only with the effect that eta, the shear viscosity of the solvent is large, in particular that the typical length scale of the swimming object, L, is very small. This is in the enumerator, L, and eta is in the denominator. Small means, in this case, that if you go to micrometers, the Reynolds number is 10 to minus 6, or 10 to minus 4, so it is practically zero. While for, say, a human body, if you swim in a swimming pool, the Reynolds number is of the order of one or larger, and for a racing car it is even much larger. If you look how bacteria swim, they swim 100 times their body length in one second, while a human only swims, if you are a good swimmer, 1.5 times your body length in one second, so bacteria manage, if you believe, this is a fair comparison for body lengths, bacteria manage to swim very quickly, and also the technique of swimming is completely different. Humans, if you are in your swimming pool, you do one breast stroke, and then you are gliding. It's inertia which drives you forward, while this doesn't work for bacteria, they swim at low Reynolds number and need another technique. And here is a famous theorem, so-called scallop theorem. This is a model of a scallop, it's a scallop if it just does this and then goes back. It works in water for a macroscopic scallop. This is a way to propel, but if you go to a very viscate liquid or to very small sizes, at low Reynolds number, it doesn't work any longer. What you do is you move forward and then if you open up again, you move backwards. So you just do this. This is not good if you want to escape a predator. You want to move. So bacteria, some of them at least, typically have corkscrew flagella in the back and they are rotating this corkscrews. And this means that the motion of the flagellum is non-reciprocal in time. What do I mean by non-reciprocal in time? Non-reciprocal in time means if you mirror the time, so if time goes in minus time, the motion is not the same as before. For a scallop, if you mirror the time, it's always the same. For rotating helix, if you mirror time, it goes the other way around, clockwise goes anti-clockwise, and so it's not the same. And that's one of the reasons why the bacteria swim very efficiently. Now there's a new development in the last decades. They say, I don't want to use mechanical motion of my limbs or whatever, of my body. And this is difficult for micro-nanoparticles anyway, since what you should do to mimic mechanical motion is do little robots that do motion like this. It's not so easy, but there are better and more efficient techniques to self-propile, to swim in a solvent. And this is how it works. The particles themselves generate a gradient of something. I will give you an example later. And then they move autonomously along this gradient, since you have a non-equilibrium situation. And this brings you to the picture of artificial model micro-strummers. And these are dominated by dissipation, since you are always at low Reynolds number, and by friction. Here I say our working horse now for such an artificial colloidal micro-strummer. It is a Janus particle. Janus is a Roman god who had two faces. So you have a colloidal sphere, micrometer sphere, and you put a metallic coating on half of it. So there is a cap, in this case gold, and say a non-metallic other part. And then it's micrometer size, several micrometers, and then you put it, that's the one idea, you put it into a reactive solvent. Of course, if you put a Janus particle in an inert solvent, it will just perform Brownian motion. There's nothing it will do else. But if you catalyze a chemical reaction at one of the surfaces, say for example it's a gold part, then something goes on on one side, which is missing on the other side, and you get an imbalance of the situation, an imbalance of forces, and that drives the particle. And in this case you use a decomposition of H2O2 into water and oxygen, and at one side we have platinum gold rods, it's a platinum side, you have oxygen that is produced, so you have little bubbles from the chemical reaction, and these bubbles more or less drive the particle to one side. Actually, the mechanism is not understood completely, even today, but you can move these particles. So you have little submarines on the micrometer scale which move on their own. You don't have to, they beat them from the outside, they do it on their own, so they are autonomously swimming or self-propelled particles. One disadvantage here is you are running out of fuel since at a certain time, after two hours, the amount of H2O2 is exhausted, so there is no fuel any longer and the particle gets slower and slower and stops. How can you get out of this fuel limitation? Okay, here's another, I think, very ingenious example that you use laser illumination to get particles running forever. And the idea is to use a non-equilibrium phase change, a fluid-fluid demixing in the solvent and then you throw the particles into that and heat them very, very little bit up. The idea is here, in this phase diagram, it is now a very good idea to use a certain mixture. It's water and lutein, lutein is stinking a lot, but at least it has a lower critical point at about room temperature and that's what you take advantage out of. At about 30 degrees, there is a phase separation from A to B. If you are in A at low temperatures, there's one phase, a homogeneous phase, if you go to B. If you heat a little bit, the system phase separates into a lutein pool and a lutein rich fluid. Now look at this picture, bottom left. You take such a Janus particle in a mixture and you laser illuminate and then the metallic part heats up a little bit. It's getting warmer there since the heat is absorbed. And then locally, you go from A to B in the phase diagram, which means you generate wetting. You go into the two phase region, which means that there's more lutein in the metallic surface than in front of the particle and this brings the solvent into flow and this makes the particle propagating on its own. That's the idea and it works and you can let the particles run forever, basically. Here are some more details. I mean, in this picture below, the laser intensity is shown, so it's not much. It's micrometer squared and if you exceed a certain threshold, I0, you bring the particle into motion and the particle velocity approximately scales linearly with the laser intensity. So you can now at which control your motion. High laser intensity, particle goes, low laser intensity stops and so on and so on. So this is one of the, as I said, working courses where many experiments by now have been performed, mainly in the group of Clemens Bechinger, who is now in Konstanz and here's a review article on all this physics of active matter, active colloidal particles, in particular what you have to take into account are fluctuations. So these particles are still Brownian and he is just an idea of what can be artificially done and also what is found in nature for real bacteria, sperm, E. coli and so on. Now I would like to bring a little bit of theory to your attention how this idea of self-propagation and friction and also the fluctuations are important. Now, we are at the microns scale, so fluctuations are important and you don't want to be killed by the fluctuations. You don't want to go on your own. And the simplest model which brings all this about, so self-propagation, friction and also fluctuations is a so-called active Brownian motion, active Brownian particles. And the equations of motion are shown here in this first block. There's a fourth equilibrium and a torque equilibrium. Let's first talk about the force equilibrium. You are normally expecting a mass times acceleration term first. This is zero since we are at Lorena's number. Everything is dominated by friction, so we have friction constant times velocity and that's equal to first of all a fluctuation force that's the right-hand side, f of t, but also an internal force that is the important one, the red one, which scales with the self-propagation velocity and is directed along the particles, say, Yano's caps. And this orientational degree of freedom in two-dimension is fluctuating with orientational noise. So you have Gaussian noise for the translation. This is f of t. You have Gaussian noise for the rotation. That is the random torque, that is g of t. And these equations are coupled via the self-propagation term. And if there is no v0, if there is no self-propagation, we are back to ordinary Brownian motion that was solved by Einstein many years ago. And what it basically says, these equations, is you have not any longer a random walk. A Brownian particle is a random walk, so you go to the left and then you don't remember and you go somewhere else to the right, right, left, left, and then you know all, on average, your mean square displacement doesn't scale with time squared, but just with time, that is diffusion. The mean square displacement scales with time. But what you have here is something like a random drive. So remember, you have a car and the driver is blind and it steers. It has a steering wheel and it has random fluctuations in the orientation where to go and it goes at very high speed. This is a dangerous concept. So you go with your car very quickly and you have random orientational motions. This is what people call a persistent random walk. You remember where you came from via the orientation degree of freedom and you may also call it a random drive. So in this active Brownian motion model, you can calculate the mean displacement, but the mean square displacement, you can calculate this in this formula and you should do a log-log plot of the mean squared displacement. You see for small times, it's linear in time. That is translational diffusion. For long times, it's diffusive again since you go on average randomly. But intermittently, for an intermediate time, you have ballistic motion and this reflects the fact that you have your velocity v0 at work and the diffusion coefficient for long times scales as v0 squared over for the rod. It's much, much larger than translational diffusion. So you can significantly enhance the diffusive motion and that is what bacteria actually do if they are searching for food. They want to know where is something and they explore the region much more efficiently than a stupid Brownian particle that is not self-propelled. That's all good. So now I'm going one step further and starting many particles, many Janus particles which are interacting and we have done simulations with a pairwise potential, in this case a WCA potential, but we have also, I should say this at this conference, done simulations with the Yuccava potentials, maybe two on the Mark Robbins who did fundamental studies on the Yuccava, many body systems with Kurt Kramer and Krest is an important paper on the phase diagram which we also used to calculate activity effects here. But anyway, many particles, classical particles, they are all self-propelled and they are interacting via a potential that is not aligning. So the particles just bump into each other. They don't align. And there is a dimensionless parameter, the so-called Peckley number that measures, say, KBT, the fluctuations over the systematic energy which you get via friction and if this is small, you have equilibrium effects. If this is large, the system is dominated by self propulsion and there is a new effect that you don't know from equilibrium physics and this is now called MIPS, Mortility Induced Phase Separation. And let me briefly explain how it comes from. Suppose you have all these particles moving and there is a triplet collision. Like a Mercedes-Benz Star configuration in B here, three particles are opposing each other in the self-propellation and then they are blocked. And they are blocked for a long time until a fortunate rotational motion brings one particle out of this, say, blockard effect which you can escape. And now there is a competition between two effects. The time it takes to deliberate yourself from this blocking configuration goes with one over the rotational diffusion. That's the typical time you need to rotate. But in this time other particles can come and collide with the cluster and make it larger and more immobile and this is the traveling time which scales with the particle density and also with the self-propellation. And if you put these two timescales equal there must be, say, a fundamentally different behavior. If particles can become free there will be no clusters if particles cannot become free. What is going on? Stop or continue? No. That's actually what happens. And here I show you two movies. No movies, but in the low-peckly number case particles will form clusters transiently but these particles will dissolve while in the high-peckly number case on the right-hand side there will be in the end one big system-spanning cluster and that is seen in the experiments and in the simulations. I will try to get at least one movie running. Everything is crashed. You can work it out with a field theory but the critical point, the question is are the exponents classical, easing-like or not, you can find analogies to thermodynamic phase transitions beautiful, so that's MIPS and that's not for passive systems since for passive systems you know once you have repulsive interactions there's never a fluid-fluid demixing. There is a critical point only comes from attraction. How much time? Ten minutes, very good. Now let me go a little bit up in Reynolds number again so up to now we had inertial and viscous effects went down to very small sizes so 10 to minus 6 where we could neglect all the inertial effects and ended up with fluctuations and viscous effects so friction and fluctuations now we go a little bit up and then we keep the term which is proportional to inertia this is mesoscale active matter and the model is now called active longevity motion and you have look at these different organisms you have scales where bacteria and cells are moving on the left-hand side but then there is a mesoscale regime where little animals like flies and little fish and bees are experiencing say inertial effects up to marine macroscopic scales where inertia is dominating so I will now go back a little bit about the inertial effects and how to generalize the equations is pretty clear now is I include in the red box here inertia for both translation and rotation and then the equations are more complicated same kind of noise that you could even introduce a systematic talk M here which brings a particle in a systematic rotation this is a circle swimmer but I will not go into this so now we go from a micro swimmer to a micro flyer now you are moving in a gas phase and there are several timescales and I cannot explain them in the remaining 10 or 9 minutes but I just say well the important timescale is a persistence time again so that's the time upon which the particle loses memory and there is a translation momentum relaxation time dd tau d that is mass over friction and if this is zero you can immediately relax if this is large the momentum very slowly relax and the same for the rotational degrees so what you can do in this model is calculate the long time diffusion again you have something like a random drive but now you have inertia and you end up again with a formula that scales with v0 squared over dd root and there is a scaling function you can calculate however it is a lower incomplete gamma function and something a combination of that it is not say standard and interestingly for passive underdamped motion this long time diffusion constant does not depend on the mass and on j but it does so if you include activity it does not depend on mass but it depends on j so on the moment of inertia and here are the high j and low j expansions of this and again what matters is persistence since the moment of inertia also makes the rotational motion slower it slows it down so you keep longer your memory and that is what brings you forward in terms of diffusion and now there is another inertial effect and maybe the movie works I don't know it should be a very nice movie it is a very very nice movie and you can tell a racing car driver to move along the corner to make a curve he or she exactly knows what to do first turn the steering wheel and then inertia will hinder the rotation but later on it will win and you go around the corner so first you steer your wheel and then the velocity follows that is what the racing car driver does and you can also see this in the inertial swimmers by defining a correlation function it is now a dynamical correlation function I correlate the velocity after a time t with the orientation before a time t and you interchange the time arguments and subtract two things so if they are completely uncorrelated this is zero but if this is positive it means that first your orientation changes and then the velocity follows this we called inertial delay this correlation function has a peak at a say certain time and the amplitude shows you the effect of inertial delay and here is an analytical formula you can work this out completely and you can test it we have tested this also against data of swimming beetles predatory beetles swimming at the water interface and they exhibit also this kind of inertial delay effect and you can do here are a couple of other papers which have to do with mass ejection or injection and active motion how to say realize that swimming beetles but also there is here dusty plasma dusty plasma are basically micron sized spheres but not embedded in the liquid but in the plasma so in the gas inertial effects play an important role and they are now first experiments for Janus particles in a plasma that confirm basically these equations now in my last minutes I would like to tell you what happens with this MIPS motility induced phase separation this Mercedes star collisions if you have inertia I normally know if you change a parameter in 95% the result is boring the expected one but in this case it wasn't I would like to tell this story to you now so the equations of motion are clear so we take this interaction potential Java or WSA doesn't matter repulsive in any case and then we write down the active longevity equations with the self propulsion velocity we are not here and what about MIPS with Sovendu Mandal and Ben Ulypian in this paper here he obtained several effects first of all inertia destroys MIPS third the cluster goes exponent is smaller than one third which it is normally for active Brownian motion so inertia changes the exponents but what you also see is you have a coexistence of two phases two different kinetic temperatures and that is surprising since you learn in thermodynamics if you have phase coexistence phase A here and phase B here the temperatures should be the same since they wouldn't be the same there is heat flow as long as the temperatures so long as the temperatures are compensated and are equal this is not the case in this non-equilibrium situation and here is hopefully a movie which works so I describe in words that you have an initially homogeneous system temperature, kinetic temperature is homogeneous and density is homogeneous and then spontaneously you get a region which becomes very cold and another region which stays hot and where it is very cold the particle density is very high that's the idea and the idea is here is a snapshot here is a snapshot the end state point of the movie that you get say a temperature inside which is very very small and the density that is shown here is very high the idea is that in the dense phase there are so many collisions that the particles cannot accelerate to obtain their terminal velocity V0 but they can do so in the gas now you can think about this is crazy so we have put forward an idea of active refrigerator which uses this effect so it cools self cooling not as a heating but as a cooling machine and there is also the fundamental question how can we describe this there is no theory up to now these are just simulation data and this is something and here is again the mechanism in the gas phase particles accelerate there are only few collisions until they have this velocity V0 they cannot do so there is so much jammed that they are completely cold and here is a simulation data for the gross exponent of the dense cluster and you see that the gross exponent significantly changes from 0 to 1 over 5 I am sorry jump the self propelled colloidal Janus particles show fascinating single and collective phenomena dominated by friction thank you very much for your attention the questions a lot I think we start with you very nice talk I just wanted to ask what prevents the continuous aggregation in the case of self rotating particles is something related to centrifugal effects like in the meteorites that both persons showed before what limits the aggregation into the clusterization of these self rotating particles ok if I understood correct I mean the end state is one big cluster the one phase separated bulky part of dense system and what limits it is the pre-scribed density you impose the density if you have a very very large system you have density and then this dictates the portion of dense phase is that was the question like in thermodynamics very nice talk do the Janus particles when they flow create a flow in the liquid afterwards so that you get correlations between the Janus particles very important and very interesting questions they do, there is an idodynamic flow field and one should take this into account if you have dense suspensions people here discriminate between pushers and pullers so if you push the liquid so if you do it with your legs you are a pusher and if you do breast strokes you are a puller so you pull the liquid these are two different hydrodynamic flow fields and actually what we did for the MIPS we neglected all this but if you take it into account it diverges normally against MIPS it doesn't want particles to have close to each other but it is a really subtle thing and can also be measured one quick educational question so the Reynolds number does not depend on the slip length or on the liquid solid friction it is just viscosity and size it is just viscosity so we assume that the slip length is much smaller than the body size and that is always even if you start including inertial effects you go down to the level scale it is questionable but for micro size particles in normal solvents that is fine there is only one length scale here no important point do you want to see an experiment yes if I get one minute to talk about that we have an experiment in our cellar so I am in an institute of theoretical physics but we have a vibrating plate where you put little plastic animals granules and then they move and they are dominated by inertia we hope to find or are beginning to find this effect in an experiment the real new trend that is that theorists are becoming experimentalists so this is really what we should ok thanks a lot thank you