 Here's the result. Ok, thank you. I would like to thank the organizers for inviting me to this very interesting conference, which is related to Frickshot. Cernost, smo bilo otročiti kundarič, so kot naši in zapotrečen boj, tukaj, če je razumil in tamo del, koost se boje, proč, je vsezrednije inzidentnej kuleibriju na mirrosk Rebeccače. In včo je razumil, tako svoj smo v zelo, vs. občinitivno, vzelo, o izmeni periodi, vs. tanju, naša nao, cinco result about what happens on a disorder landscape as the one that is in this image. So, my name is Pietro Tjernan from the University of Barcelona as the chair said. You are all welcome to visit me. Basically, it's a very pleasant place. And most of the experiment, this is an experimental tool, has been pursued by a postdoc of mine which is now in Switzerland, Roufleht Stop, it's the first auto. počešel sem početno kolišnje z teoreticijem in sem osvojila, da je to vse začela. Tako, prezivno, to je to, da je to tukaj zelo v dvej pavni. Prvja pavna je zelo v rečenju zelo, nekaj zelo, da je to, in druga pavna je, da je to, da je to vse začela, pa prezivno, da je to, da je to, da sem početno, da je to, da je to, So, how do we travel these magnetic colloids? So, here you see, let me stop the video, a real time experimental video, where you have a large collection of microscale particles, the A size is 1 micron, so your thermal fluctuation are important, but the magnetic interaction with the underlight substrate that you see with these parallel stripes, vzoutrem, da vzoutrjem vzoutrem, je zelo tako nej strane, dar te nekaj vzoutrjeni sem vzoutrjeni. In, zelo, da videlem toga vzoutrjena, ker smo bojteni spetaljne teknika, da smo vzoutrjena kolaritzacijenja mikroskopir, je to koncentrjne potenče, je to nekaj načinji, nekaj nekaj načinji, nekaj načinji potenče, nekaj nekaj nekaj načinji potenče, je to so nekaj načinji potenče, zelo zelo, ki je zelo vzelo na stavljenj sprijev. Zelo se vse prijev da je ničske potenzije, ki je tudi vzelo na vsega zelo, ki je kaj se predaj tega zelo, in ki je bilo vzelo, da je to zelo, da se prijev, da je tudi vzelo, da je tega zelo. To je vzelo na vsega zelo, da je tudi vzelo, da je to vzelo. To je vzelo na vsega zelo, tako, da je dobrojno vkostan spid, tako, to je vse bojstvih možnosti, da je zelo spodljeno, da je vse spodljeno, in je to počutno začeljno. In danes je bilo in pozosto, da je vse zelo, da je začeljno, in da je začeljno, da je vse odrata. Zato, je to vse veče počutno, da počutno, zelo spodljeno, vse je odrata vse, periodicne potenče. Vse zelo, da se vse zelo, vzeliš v nekaj komplejno različ. Prejmo se o sistem. Srečen sem vsega kristala. Zdaj je tudi vsega vsega vsega vsega. Zdaj je vsega vsega in vsega vsega. Tudi je vsega vsega in vsega. Zdaj se vsega vsega izgleda, kako smo vsega vsega vsega, zelo se vsega vsega vsega vsega vsega. Vsega vsega vsega vsega vsega. in tukaj je skomatičnja krozsekšnja. Svetičnih je karakterizati v zelo, kaj je tukaj v zelo. Svetičnih je kompozivati v magnetizacijne domene, ki je v oposite magnetizacije. Tukaj je tukaj vzelo, kaj je vzelo, kaj je magnetizacija vecto rotacija. Vzelo je tukaj vzelo, stavljam vzelo in da sem na nekaj pridem vzelo, ki je zelo učinjala, nekaj nekaj potencijal, ki se počusti, da je to zelo učinjala. To, da je napoljeno vzelo. In, da bomo zelo... Ešte, da sem napoljeno, oče sem. Tukaj počusti je, da so se vzelo na zelo, Sledno je velikga skala in tova magnetija, s tvojim lagom tudi in prič tvoj del. Vsi in vse sestim vse vse voljila, mrnje v vseh ravodnih nekaj. Laji vse sei vstaj 2.6 vse, vseh po freelancej. Danes privoljamo vzelo bolj, genulje je tudi rata, magnetijne vse. Zelo vse to je vzelo to, tudi v rata vseh vseh vseh rata, v počke, na kratičnih, zelo je tudi karali, tako v kratičnih, zelo je bilo počkaj, da se zelo je održivati, da se održivati, da se održivati, tako da se održivati, in da se održivati, je vsebo vsebo, adiabatik transport, možno, da se održivati, in da se održivati, na to, da se održivati, izgleda je noželj energij, in se zelo se počutite v počutku. Zato se možete vzvečiti, da je to vzvečite, da vzvečite, da je to vzvečite, da je potenčena, ki je generativa na obradi, počutite se počutite, in da je potenčena, kaj je delaj odrečen, to je proporčeno na frekvencij delovih vsev, tako, ki nekaj je vsev, se je spravljena in vsev. Vse je tudi vsev, da pogledajte vsev, da ste z salu površtni, znači da nekaj je vsev, neko je zelo izgleda, nekaj se je začel, in nekaj je vsev začel, da jste z vsev način, z vsev in vsev. The fact, basically you can describe the synchronization process by using another type equation. Okay, this is basically one dimensional system. The nice thing is that you can generate also two dimensional structure like lattices, basically of magnetic bubbles. These are ferromagnetic domains that have all the same magnetization directions. So these are pointing upward. And they are immersed in a film of opposite magnetization directions. vse je tudi daželno potenčnega z vse silintrične domene vzveč na tudi, da se vse trangularne latiče vzveč. Vse je tudi za, da se vzvečen sem vse st tricked pattern, iz kaj sem izvajal, v zvaj trengularne latiče. Vse zrečen sem zelo vzvečen, da sem vse zelo vzvečen, da se pomečnega zelo vzvečen. Vse je biti llarger, are 2.8 microns, moving across this basically two-dimensional lattice of cylindrical domains. Of course, you can change the direction of your rotating field, make the particle going up down, so going all out of the two-dimensional space, and if you measure the average flux, the colloidal flow, basically you have clearly two regime, a synchronous regime where ki se vse vse vsega nekaj tega, je prišel in na narednjih 1, when you increase frequencies so you go too fast, the particle lose the phase with the traveling wave and they just go backward so the average speed decreases and you have a sharp transition between both of them. This can be easily described in term of a synchronization process. Now, related to basically friction and I go to the first part of my talk, ...ga bo še pa je tudi flaske, ali je nekih kratičnjih z še prišličenujem... ...z nekih, da sem illuminacijen... ...vej z njega razporovali. In je tudi, da in ne ma večjavak otari, ...in je tudi, da je večjavak ta z까지, ...ko je nekaj, da se in držje držete na kristolografice. i na sezne odnešene in je jednogodne vsove, kot, da je nekaj dužne učin, v početnih učinačiju idejo iskandlje. Salo, legao, da je to porudnje, in prikač nadejte legao. Zelo je, da je zelo zelo. In zelo je, da je pripačna �očnaja in bih nazivati p有點ne početnje, in zelo ste na ten del. Vse natravca napal se parti u nekaj kristologiarne odzaj. Vso napal nosi se pred vetanski platov, kaj ga izvistim bila začasno vzolite s vzelo irte. Zato je začasno vzolite kristologirne odzaj na tančenih teta. Teta je taz vzolit, na ključa prijev. In taz je začasno karist. Vse je vse kraten, kaj ga najčelreato in nešto je vsega kaj je izgledno. In there have been also other very nice experiment. Sorry maybe I go too fast. I mean, they were done basically in 2003, where they use this directional locking to sort different types of colloids, for example of particles. So it's a way basically give rise also to technological application, or quite recently in the group of Clemens Bakinger, Bacically, we will hear a talk this afternoon on that, so we have also directional locking of a larger cluster made of colloids on top of a periodic substrate. So this is a very nice phenomena that has been explored basically at the single particle level or at the large cluster where you have effect of commensurability between basically the cluster and the underlying pattern. But I would say that quite not really recently, sometimes ago, but in 2008, there was an article where they showed the possibility also to have a collative directional locking. So the fact that not only at the level of individual particles, particles lock towards a crystallographic direction, but can be also that when you have a many body system where there are particles that repel each other, they can also even lock along a certain crystallographic direction. And also a colleague of mine in Los Alamos, Charles Reich Reijher, they show with numerical simulation on a vortex system, which is similar basically to a colloidal one on the collective level, because these are also overdone particles. The interaction is a bit different than my microscopic level, but I will tell you just what is the phenomena. So they see that basically when they have an underlying pinning, which is made by a nonicom pattern, and they have colloid, basically vortices that strongly interact between each other, when they drive with a constant force, can be that for certain value of the force, basically you can lock all the lattice along a certain direction, and you can even have vortices, the slides upward, or vortices, the slides downward. And these basically appear as bifurcation, like in the velocity as a function of the driving force. Of course then, when you reach a critical value of the driving force, the pinning potential basically is an important and dull particle flow along the driving direction. And this is basically due to spontaneous symmetry breaking, because if you perform again, this was numerical simulation, the simulation basically starts again, the direction they choose, whatever it is upward or downward, is totally random in this case. Let me tell you that the lattice is oriented in such a way that the two main crystallographic directions are basically one, of course perpendicular to the other, and they intersect the driving direction. So if you have directional locking, you either go up or you either go down. And we try to do the same with our two-dimensional pattern of magnetic colloids. In fact, we get this triangular lattice, and we orient the triangular lattice in such a way that basically the driving direction exactly intercepts two crystallographic axes. In this case, we are driving the particles from right to left, and we have these two crystallographic axes, the green and red ones, so minus one zero at zero minus one, that exactly basically are at the same distance respect to the direction of our driving. It's not the constant force, it's the direction of our rotating magnetic field, which generates this kind of traveling wave. Of course, for a two-dimensional lattice of ferromagnetic bubbles, the two-dimensional periodic potential is a bit more complicated in the previous case. So here you have a time sequence, basically of magnetostatic calculation of this two-dimensional periodic potential that show, depending, this is one field period, depending on the orientation of the applied field, you can have the energy minima, which are basically in the color red, they are either at the center of the magnetic bubbles, or they can appear in the interstitial regions. So this is taking the count, basically summing up the field of all the bubbles that are like this in a uniform magnetized periodic potential. I will give you more details, of course, if you are interested, during the coffee break. This is no problem. But nevertheless, during one period of the rotating field, a particle that is initially placed here, basically at the center of the bubbles, so it can go, basically here there should be, this is invert, but let me tell you that it is initially placed here, then basically because this image should go here, it's okay. Then there are six minima that appear at the interstitial region, while the central region becomes an energy, basically is energetically higher. So the colloids have two choices, either it can go upward or can go downward. Then it can end up at the end in one of the two bubbles that are basically nearest neighbors, so it can either go upward or downward. So now you have a real time video of when we are driving these magnetic colloids, a gross, a large area of these two dimensional periodic potential of bubbles. As you can see, at the level of single particles, the particle just perform random escaration along the transversal direction. So in average, they have a constant speed along the x direction, so from basically right to left, but randomly they can either go up or either go down, because small thermal fluctuation can decide which of these two root can be basically undertaken by the driven colloids. But what we find out, and this is related to this collective directional locking, is that when increased density, the amount of particle within the observation area, so we observe the following case. Sometimes the particle form clusters, and this cluster, because the time average interaction are a bit attractive, so this cluster trend to polarites along a certain crystallographic axis. While individual particles, you can see here, they perform random escaration either up or either down, trains of colloids either go up or either go down. So they can basically become polarites, and they choose to lock along one crystallographic direction. And in fact, since these are colloids, basically we can use simple optical microscopy to basically extract all the relevant degree of freedom, basically the particle position and extract all the physics. You can calculate everything there. And in fact, as you can see, when you increase the density, this phenomenon becomes more and more evident. So let me tell you, for example, here is the trajectory of one colloids along a certain time periods that perform randomly upward and downward. And then downstairs there is a trajectory of particles in a large cluster that just polarites along the upward direction. And effectively, we change the density, basically we measure the trajectory, we find out that if we plot the velocity, the average velocity of our collection of colloids, as a function of the density of the system, we find this before question like cluster is not where, which is due to this spontaneous symmetric breaking. So here we have branches velocity that go upward along the positive direction, so we are now driving the colloids, let me tell you we are driving the colloids from right to left. So we have here in blue as a blue scatter data, the average velocity along the driving direction, which is negative as it should be, and then as a black point, basically experimental data of the driving direction along the transversal direction, basically perpendicular to the driving one, which can be either positive or negative, depending whether the colloidal trains are polarized along the upward direction or downward direction, and we see basically that both situation occurs. And this is due to a spontaneous dynamical symmetry breaking. If I stop the field, repeat the experiment, my colloidal trains can either go downwards or upward, doesn't it? This basically depends of small disorder present in the system on thermal fluctuation. Of course, when you increase the density at some point, when you reach a very high dense system, so the particles now are in a cage, they have a lot of nearest neighbors, they cannot polarize anymore, they all basically, this become a moving solid, they just move at constant speed, so the longitudinal velocity becomes zero and it just move along basically the driving direction. So with this basically just tell you briefly that one can break this symmetric situation by applying a constant bias field along one direction, which make basically one direction prefered respect to the other, as it is shown here. You can find more information on this work in this recent publication that appeared and was done in collaboration with Arthur Straube in Berlin, that is a theoretician that allows us also to understand this time averaging magnetic interaction. So with this I basically finished the first part of my talk. I tell you a bit more about disorder system, that it's more complex but also more similar to real life cases. So we find out a way basically to disorder this periodic lattice of these triangular lattice of bubbles. So it's an experimental trick that is basically based on changing a bit the way we create this pattern by using high-frequency magnetic field, but at the end we can create an exotic-like phases, where basically we have a series of crystalline domains of bubbles, but they are basically separated by grain boundaries, that enclose different crystallographic directions. So we can introduce in our system a controller the degree of randomness of disorder. In fact we can characterize by using all the standard basically tools, which are like calculating the pyre correlation function or the bond correlation function, that is basically the orientation of the six neighbors in a placket with respect to the nearest wall. And actually we find out that the phase looked like an exotic wall. For example, people expert in the exotic system would say, ok, but your system is nevertheless relatively finite. You need a quite larger length scale to be able to infer the exponent. I totally agree, but nevertheless it's a way that we use to characterize the degree of randomness in the system, which is basically the fact that this bond correlation function that you have here decays algebraically in this disorder case with a certain exponent. That we use to characterize the degree of randomness. Of course, if it's totally flat, we have a perfect crystal, a defect free as the one on this image here. On the other end, if start to decay, but not basically become not exponential one, like in a liquid case, so we have an exotic like structure. Now on a disorder system situations start to become also a bit more complicated. Still you have these trains, but the train do not polarize anymore, because of course they can encounter these grime boundaries, get trapped there, again they can get destroyed close to this grime boundary. So we measure, let me, how long time, I'm still left, 5 minutes. Ok, with discussion, so we'll try to speed up, ok, thanks. So basically we measure the average speed of our magnetic colloid as a function of the normalized density, and we find basically two surprising features. The first one is that we drive our colloids now in the asynchronous regime, so the frequency is very fast. So we find that as we increase density, they speed up, there is a speed up effect, and then there is a slow down as very high density, which is due to a disorder induced jamming. It's an effect, it's due to the disorder itself. Let me tell you just that basically we can explain, we have a model, this system by using a simplified model, this work has been done in collaboration with Dominic Lips and Philip Mas at Osnabrug University, and I will skip this because of the time constraint. Nevertheless, there is the following, at some point we were able to explain the speed up effect, and in order to explain also the disorder induced jamming, we switch to a totally different type of modeling, is there to take brute force, take the interaction, this complex magnetic interaction, the Doppler interaction, hydrodynamics and so on. We just switch to a lattice gas model, where we assign certain probability to the particle to jams, and the certain probability to the particles, once they become cluster, to move faster with respect to their neighbors. Ok, so we pursue Monte Carlo simulation, and the nice thing that is this relatively simple lattice gas model, is able to capture very well the experimental data. Actually, you can see here that we have a scattered data, basically the normalize flux of the average speed, normalize flux on the left, average speed on the right, of our colloys as a function of the density, so increasing density, increasing interaction, particle see each other and so on, with the continuous line this lattice gas model that is obtained from Monte Carlo simulation. So, I won't stay more, because I would like to have also questions from the audience. Let me tell you that there are different future directions that we are exploring. I would like to thank many collaborators that helped us to understand from the theoretical side this work and the funding agency and especially you for the attention. We will be really happy to take all your questions. The next lecture. Thank you for your nice talk. In the last part it was a bit quick for me. So, eta6 is the exponent for the bond orientation or the decay, right? Yeah. Why is it... Normally you have a range from 0.05 to 0.6. How do you manage this? How do you control eta6? Okay. We basically different experiments, different field, different field that we apply to prepare the field. So, we somehow control the way that we go from a very order to a disorder one. So, we track the position of the bubbles before making the colloids of that and we calculate the bond orientation of order, basically. We find out... Really in a controlled way. So, you can really say, arbitrary exponent you can... Is that what you said? Well, we did... We did some experiment. We find this exponent and... Okay. It's a bit the other way around. But, I mean... Peter came out so you can do it. It's amazing that it's... That it's changing such a lot. Yeah. Yeah, we can change it a lot, but there is also the things that our system is not huge. So, this can be also debated and then at the end this become... You know... Come to the...