 So it's 3 o'clock. It's a great, great pleasure for me to really welcome this. And it's the first time for me to welcome a professor here for this presidential lecture series. And the series started, I think, in 2018 to really invite prestigious professors here to engage a larger community. Like, you know, it lives in the culture of East and develop it further across the different disciplines. And I think we have had a good series of these type of lectures. And we are going to enjoy one, I am sure, here today as well. And so it is, as I said, it's a real pressure for me to also be able to say thank you and welcome to Professor Sid Nagel from the University of Chicago. And I think you are an example of definitely a professor that can live up to this engagement and to really spread the excitement of science. And you have also, when you are here, and as I hope that most of the presidential lectures are also giving more to specific science discussions during your time that you visit. And I hope that that's going to inspire also more collaborations and that you will be a little bit of an ambassador for us to get people to come over here more and more. So I want to thank you for that. And I just want to give now the word over to the host for this lecture. So this is the professor, Mr. Bandy, that is from Soft Matter Physics. And please take it over. Thank you, President Makidis. Good afternoon, everyone. My name is Mahesh. I'm on the faculty here at OIST. There's a puzzle I try to solve whenever I come in contact with any scientist, which is to figure out their one trick. I believe each one of us is a one-trick pony, and I'm trying to figure out what is the scientist's one trick. And in case of Professor Sid Nagel, I must admit failure. He defies classification. I couldn't figure out his one trick because Sid works in a variety of stuff, from fluids to granular materials. But the most impressive thing about Sid is perhaps how he takes commonplace phenomena and elucidates or shows us a view of the world we did not observe. Because these phenomena are commonplace, it's like familiarity breeds contempt, but not quite contempt in this case. Because we see them in commonplace settings, we assume we understand them. But there's a difference between knowing and understanding. And that is where Sid brings a point of view and shines light on a view of the world that we have missed. And by way of more formal introduction, Professor Nagel is the Stein-Freiler Distinguished Service Professor at the University of Chicago. He received his bachelor's from the University of Columbia. Sorry, Columbia University. University of Columbia would be in Columbia. Sorry. His PhD was from Princeton, and he was a post-doctoral fellow at Brown University, following which he moved to the University of Chicago, which has been his academic home ever since. His contributions to science have been recognized with several honors. He is a fellow of the American Physical Society and the American Association for the Advancement of Science. He is an elected fellow of the National Academy of Sciences of the USA and the American Philosophical Society. He's won the Oliver Buckley Prize in Condensed Matter Physics given by the American Physical Society. And most recently, he was awarded the APS Medal for Distinguished Research Excellence. He's an excellent educator, and we are actually lucky to have one of his most recent mentees as a post-doc in my group. So I don't want to keep you boring with my spiel. I want to hand over to Sid, and he has some demos for us as well, so we are definitely going to be entertained. I hope we learn something as well. Thank you. Thank you. Well, thank you, President Marquettez, and also Mahesh for incredible hosting here for the past week. And so it's really been a great pleasure to be here. What I'd like to tell you about today is some work that we've been doing over the years on patterns and structures formation in nature. And so what I want to be specifically talking about is how the structure emerges. So it's going to be a little bit focusing on dynamics of what happens. And so the focus will be on instabilities and the singular dynamics that creates these patterns and structures that I'm going to be telling you about. So the first thing I should say is, well, all these things are going to be done in fluids. And so I should just give you just a tiny little flavor of why fluids are so important to us and to me in my lab. And the first thing is that fluids are a test bed for a whole bunch of basic issues in science. And so I can't think of more basic issues than how do we understand disordered matter? We're really good at physicists at understanding crystals and things that are very well-ordered. But when it comes to disorder, we get kind of stuck and we don't really know what are the principles or how do we study this. Another question would be, how do you study things that are very nonlinear? So you have transitions, dynamic transitions, singularities, which I'll be talking a little bit about today. These are, again, things which are a little bit farther from what we are typically taught in our physics courses. The one that I'm most fond of is the third one here, which is far from equilibrium behavior. And if you think about that, physicists really know a lot about equilibrium phenomena. And so if I gave you a box of gas, I would be able to tell you everything about that box of gas. I mean, a boy who's stiff with everything I could tell you about it, because it's an equilibrium. And we know how to treat things that are in equilibrium. But most things around us are not in equilibrium. I mean, you look outside the atmosphere is not in equilibrium. I look out at you and I see all of you and you're not in equilibrium. If you were in equilibrium, you'd be dead. And that would be a very boring kind of existence. So it's being far from equilibrium that allows biology. So one way of thinking about biology is to say it's what's necessary to prevent us from reaching equilibrium behavior. And so in all of this, you get patterns. And I also want to emphasize that these fluids actually are important because they also appear on all length scales. And so you can think of the smallest scale of the core clue on plasmas, or that's shown to be a liquid-like behavior. You go up and Bohr told us that the nucleus of an atom was a liquid drop. You can go out into space and you see gas clouds. And these are, again, things where the stars are formed. And so you get this from cosmological down to the really elementary particle behavior is where fluids occur. And then another thing that's important to a lot of the work in what we've been hearing about in our conference this week has been rigidity formation. And you get flow versus rigidity in fluids. And so you can go from the gas to the glass, where, again, this thing becomes stationary and you can no longer move the particles. And so these are some of the reasons why fluids are such a great test bed for so many different kinds of physics. What I'm particularly interested in here is that they also are a great place to see surprises. And these are surprises that are all around us. And they really are these behaviors of the fluid which give us what I like to call the texture of our world. It's a texture which makes it interesting to us. And so it's elegant. And this elegant evokes appreciation. And then there's this quote from Plato. The philosophy begins in wonder. And I like to think that, well, physics also begins in wonder, at least physics of the kind of variety that I'm involved in. And so this is part of why I think this is such a wonderful subject to be able to tell you about today. So I'm going to start off with one kind of structure formation. And so this is what's called dilation symmetry and penetration of space. And so you see this in many different geysers. And so what is the point here as well? You take something like this tree pattern and you look in closely. And if you expand that back out to the size of this whole photograph, you're not really sure whether you're looking at the small part of the tree or the larger tree. These things are similar at these different scales. This on the right is a river network, again, taken from some altitude. I don't know what altitude. But again, if you focused in closer, you would see finer and finer rivulets. Your blood vessels also have something of this behavior and then lightning strikes, of course. So what I want to show you is another kind of behavior. And so this is where this appears. And so this is in this piece of plastic. And I'll try to show this to you in a minute. But what was done to this piece of plastic was that this plastic was stuck at the front end of an electronic accelerator. And it was bashed with electrons. So this thing was totally filled with electrons. And then at this point here, you see a tiny little hole where someone had stuck a nail into this and then grounded it. And all those electrons were repelling each other and tried to get out as fast as they possibly could. And they created this pattern. And so I don't know if you can see that. So here is where they're coming out. Whoops, here. And you see all of these patterns from here, all ending up at the end point. But if you look at closer, you'll see that, oh, you can see. It really gets fine feathered things, more and more of these things as you look closer and closer into this block of material. And so maybe I'll just pass this around so that you can all see it. But it's really a gorgeous piece of physics. So one of the things that we wanted to do was, OK, if you have that as something that you can show people and you try to get them excited in science or you show someone in a science museum, something like that, they might think that's really beautiful and want to do it. But we don't have an electronic accelerator for them to play with and make their own. So that was something that we wanted to do was to figure out how could we get people to be able to make their own patterns that had something of that kind of shape. And so the idea here was, well, we can do this with fluids. And so what I'm going to do here is perhaps the world's most boring experiment. And so I take this plastic sheet and I'm going to take another plastic sheet and I'm going to put it on top of it. And the most boring part of the experiment is this. It just goes out in this really, really boring circle, disk. How could be more boring than that? But the less, oops, you didn't see that. You can see that what you were able to get here is a whole set of patterns that come out in the same kind of behavior as we just saw in the case of the thing that I'm passing around, which is called Liechtenberg figures. OK, so this is a way of being able to see these patterns. That's a fit. OK, so this is a way of being able to see these patterns and you get them right in front of you and you can make them yourself. It's easy. You can go home tonight with just butter between two glass plates and pull it apart and you'll see something very similar to what I just made for you here. So what I want to tell you a little bit about as well, how do we try and study these things at a more scientific level? So I demonstrated this and I want to now say, OK, so what do you get to do? And so the idea here is that this is a occurs because there is this fundamental instability fluids, which is called the viscous fingering instability. And you can see this fairly easily. The idea here is that you take two glass plates, they're smooth, parallel. There's a hole in the middle of one in which you inject the fluid. So there's an outer fluid here and there's an inner fluid. And if the inner fluid is more viscous than the outer fluid, it does that boring experiment that just showed you. That is, that red blob just went out in a circle. But if you had the inner fluid being the low viscosity fluid invading the higher viscosity fluid, then you get that kind of structure that I just showed you. And so here is a movie of that. So we've already put in the outer fluid and we're going to put in a dyed blue inner fluid and we'll see what happens in this case. And so again, you get something that, well, I don't know about you, but I find these things really mesmerizingly lovely. And it's unstable. And what causes the instability? Well, it's the fact that I told you about the inner fluid is less viscous than the outer fluid. But the other thing that's very important about this is there's a surface tension between these two fluids. And if this surface tension is, what does surface tension do? Surface tension tries to keep things from becoming too sharp. And so if you have a lot of surface tension, you would think these things will be rather blunt. But if you have lower and lower surface tension, oh, it's easier for these fluids to penetrate one another. And so what we want to do is see, well, what is the endpoint of this? So if we took two fluids that had no surface tension between them, what do you see? And so this is what we see if we have surface tension. And so this is a set of images of the same experiment done with different fluids. The parameter here is the viscosity ratio, so the inner fluid, the viscosity of the outer fluid. And it's increasing up to this point. And you see that one thing that's happening is that you're getting this interior section getting bigger but now what we want to see, if we did exactly the same thing, same viscosities between the two fluids, but without the surface tension, what do you see? And this is what we saw, that you see something that kind of looks a bit similar. But look at this. This is now more stable than the one above. This has much shorter fingers than the fingers above it, which have everything the same except that it has surface tension there. This has no surface tension. And when you get over to this side, this thing is completely stable. It has no fingers whatsoever. So I'm telling you this now, and so I hope you say, oh, that's surprising because he tells me about it, but we really expect it to be able to see lots of very sharp fingers. And see something about how these sharp fingers multiplied and got bigger and bigger as we went in this direction, and it did exactly the opposite. And so this is something I find, oh, how did that happen? Why does something behave exactly the opposite from what we expected? And so this is going to be a theme in this talk of how things are constantly able to surprise us. So what I want to point out is that, OK, looking at these and you look a little closely, you see that this means that there's a new regime of behavior in this kind of system. And so I'm going to show a movie on the left, which is what we would see for this low viscosity ratio fluid. And so this is what we've kind of seen before. I showed that to you on that first movie, and you see it forms these fingers, and these fingers then break up and form other fingers. We break up and form other fingers on an infinitum. But now I want to do it at this other end of the spectrum, where the viscosity ratio is much larger. It's closer to one, closer to the point where it should become more stable. And this is what we see. And that's kind of bizarre. Look at that thing. It grew, but it no longer split apart. We got one finger, and then this instability turned itself off. And it no longer is able to create another instability on top of the one that you saw, even though this wavelength is much bigger than when it started when it first started to finger. So this is a strange thing. It's a different kind of thing. And I really object to calling these fingers because they're really stubby things, and so they're more like toes. And so they're little stubby toes that come out at the edge of this pattern. And once a toe forms, it turns off that instability, and it no longer splits. And we no longer get this finger upon finger upon finger. We don't get new generations of fingers forming. So why is this kind of an interesting thing for us? And so I want to remind you of one other kind of phenomena that we're all very familiar with, and so this crosses over into biology. And we all know about little kids, mammals. They start off at one size. They're born, and then they grow, and they grow, and they grow. But they kind of look the same from the small to the large, from the baby to the adult. And so here are pictures of a baby and an adult. And OK, the head is maybe a little bit bigger for the baby to the rest of the body proportions, but basically it's the same thing. And basically, you know that after a year or two, you can recognize a baby and the adult. I mean, you can recognize which pictures were of any particular individual. And so why do I tell you about this? Well, this is a symmetry that appears in biology. It's proportional growth. That is, everything grows, but the fingers grow as well, the hands grow as well, the legs grow as well, the head grows as well. Everything grows, but kind of proportional to one another. And this is something that if you think about it, well, it appears everywhere in biology. All babies basically do this in mammals, certainly. And are there any physical examples of this? And I can't think of any until we looked at this problem that I just showed you, in this regime of the toe formation. And so what this is, is three images of this pattern in a process formation. And so this is smaller, it got bigger, it got bigger, and so this is different scales. And what I'm going to do is I'm going to blow up the red box to be the same size as the black box, which can be also blown up to be the same size as the blue box. And if you look at that, then you see that now these things are essentially indistinguishable from each other. You see all the same little bits and pieces around each of these fingers. The fingers retain their behavior. They just all got bigger. They all got bigger proportional to the total radius of the system. So this is an example of something that shows this idea of proportionate growth but in a purely physical system. And having it in a purely physical system means it's something that you can begin to address with physical concepts, not having to rely on biology to be the process that makes this occur. And so this is the example of proportionate growth in a physical system. OK, so now I want to go over to another question, which is we looked at this pattern formation, and it was the interface between the inner fluid and the outer fluid. And this started off very smooth and then became rougher and rougher and rougher as things progressed. And clearly, the surfaces interfaces matter. And so what I'm going to be interested in now is things breaking apart in here. And so I'm going to give you two examples. One is structures on fluids, surfaces, and the other is liquid fission. And so the first example is one that we did with Kaito, who is here sitting over there. And so she is now here, as you mentioned, and so I'm so pleased to get to see her again. And so the idea here is that you take particles and you put them on the surface of water. And so these are fairly dense at this point. And what she's going to do is now pull the upper, pull her on this thing, but on the one above to the right. And so that's just going to expand this set of particles that are in there. And so I just wanted to see what happens. So here's the movie and this thing starts to expand. And I don't know about you, but I find that such a gorgeous set of structures. I don't know how to begin to describe it. What is it that's going on? What am I seeing here that makes this so distinctive? It's certainly a distinctive pattern, but what is it about this that makes it distinctive? And so this is what Kaito set out to try to understand. And so the first thing about this was, OK, you look at that and it's uniform. It's broken up. It has single particles next to one another. If she does this at a slower speed, and so this is coming out, but it's much slower, but you can see all of the structure is subtly different from what it is up above. That these things are forming rifts in these otherwise rafts. So this is rifts and rafts of this. And so this now has the same features, but at a much coarser scale. And so what's going on here? So that was what she tried to do. And so this is a competition between the attraction between these particles and the expansion of that fluid underneath, the fluid surface that's pulling it apart. And so if you look at this, you look at these different pulling speeds. And you see that this pulling velocity controls the cluster size of these things. And so you pull it very slowly. And the thing hardly changes it all from its initial state. You pull it fast. And you see kind of single threaded sets of particles. And so this is the control parameter. And this allowed her to be able to figure out what goes on. And so what is this all about? Well, where does this lead us is, again, something that crosses boundaries into other fields. And so this is kind of the big bang in a bathtub. So if you think about what is the particle interaction between these particles, it's the same as gravity but in two dimensions. It's 1 over r rather than 1 over r squared, but this is a two-dimensional case. And so if she builds this, which is now expanding in all directions, we again get the same kind of features. It's, again, a lovely set of features here. And so this is kind of another feature that I want to show partly because she's here. And so you can go and ask her everything you want to about this experiment. But I think it's another good example of you see these structures on one scale, but they are relevant at very, very different scales. And so you can think of this as a real experiment that may tell you something about nonlinear effects or as time goes on in a gravitational pulling medium. So this is one example of things breaking apart. The second example that I want to spend a little bit more time on is how a drop of liquid breaks apart. And so the question here is, we have a liquid drop. It's hanging from a platform on top. And it's gathering a little bit more fluid at a time. And so it's getting heavier and heavier. And at some point, it goes unstable and starts to fall. And we have this picture. And if I had taken a picture of just a fraction of a second later, this drop would have been disconnected from this neck of fluid here. So clearly, there's a transition here. From a mathematical sense, this is a topological change. So this is a transition between a singular connected object to two separate objects. But what I'm more interested in here is the fact that, well, what does it mean to break apart? It means that this neck here has got to shrink and shrink and shrink and shrink until it's zero radius. If it didn't get to zero radius, it should be connected. So the fact that it disconnects means that this neck here had to be at some point here where the radius of this is going to zero. So this is a, the radius goes to zero. And the one thing I'll tell you that we should know about fluids is that there is a difference in the pressure inside the fluid to outside the fluid, which is simply proportional to this thing called surface tension, which I already told you about. The thing is try to hold the liquid together, times the curvature of the surface. The curvature of the surface is one over the radius of curvature. So that means at this point where this neck is getting smaller and smaller, this pressure is going as one over that radius. So it's getting larger and larger. And so at the point of break up, this thing is going to diverge, that it's going to get incredibly large, the pressure difference here. So I'm getting incredible forcing on this thing just as this piece breaks apart. And how do we understand this? I mean, it isn't as if we don't understand the Navier-Stokes equations, the equations that tell us what the behavior of a liquid is. It's that they are miserable equations to try to solve. No one knows particularly how to solve them. And so you have to try and figure out what is going on. So what you do with this is you stick it on a computer and you try to iterate it. And you get it at some point. And then you say, OK, I want to get closer. So you work a little harder to get closer. And you have to work harder because you have to get all the points in this neck, which is getting finer and finer. And still keep the rest of this sphere also compute that properly as well. And so you've got a little closer. And now I want to get even closer still. So I work harder. I want to get closer. But then I want to get closer. So I get harder, closer. And you see what the problem is that no matter how hard I work, I'm not going to get there. It's in Zeno's paradox all over again. I work harder. And I get closer, harder, closer, harder, closer. But I never get to the other side of the singularity. But I look outside my window and there's a drop hanging. And then it just falls. It didn't think, how am I going to do this? It just did it. And the fact that it knows how to do it. And as physicists, we don't know what was going on. What was important means that there's an important piece of physics that we didn't understand. And so this is what this study was all about. To try to figure out, what is it? How do you treat a singularity like this where something is blowing up right in the middle of your experiment? In this case, this curvature blows up or the pressure difference blows up. And so again, this is something I want to keep emphasizing. It appears on all length scales. I mean, I told you about fluids in the nucleus of an atom. It's supposed to be a water drop. That's what Bohr told us. Well, nuclei fission, which means they break apart. That's the same thing as we just saw in that drop breaking apart. How does the nucleus fission? At the cosmic scale, these are probably the most famous picture from the Hubble Space Telescope, which are these gas pillars in which you have star formation. In order to get star formation, this gas here had to get compact in another region. It had to get compact in nothing in between. So again, that's the same idea of regaining these two things. And the part in between has to disappear. So it's again this idea of that singularity is appearing right in the middle of the star formation. And in order to get the star formation, you have to understand something about how that takes place. And so again, this is on all length scales. It's just that in the lab, I get to look at this at a little drop of water. And that is a lot easier to do than having to build a space telescope. So how do we think about this? And so the idea here is that we have a drop of liquid and start to fall. And I want to ask the following question. Suppose I have a cylinder of this fluid. I want to ask, is that cylinder stable? And you all know the answer. No, I just told you it's going to want to come into a sphere. That's the idea of what surface tension is doing. It's trying to make as spherical as possible. So this less surface area as possible, and that's going to be a sphere. But I'm not going to allow that kind of instability to happen. So I'm going to hold it at the two ends so it can't come in. So if I hold it at the two ends so it can't come in, then I ask, OK, now is that cylinder stable? And the issue is, well, if I deform it ever so slightly, can I deform it in such a way that it has less surface area than this one while still keeping the volume fixed? That is, I can't change the volume. The volume of the water is the same. The liquid is the same in both cases. But does this have less surface area than this? And it's a calculus problem that we can do on good days. And what you find if you do this problem is that the surface area going from here to here actually decreases if the length is long enough. If the length is larger than this original circumference. And so this is one of the standard fluid dynamics instabilities. This is called the Rayleigh Plateau instability. That is why cylinders or jets of fluid break up into drops. OK, so have you seen this? And so you can see this quite easily. And so I'm going to ask you to take your fingers, stick it in your mouth, and get some spit on it. And OK, tonight, go home to your bathroom. Close the door. Make it so that no one else can see what you're doing. Close it. Lock it. And then when no one is looking, stick your finger in your mouth. Get some saliva between your fingers and spread it out. And what you'll see is a little thread. And in the middle, there's a little ball that comes in. And that's this Rayleigh Plateau instability. Now, I kind of expected that you would all be too shy to do this in public. Although I'm not shy. I don't know why you couldn't. But anyway, you didn't do it. So I wanted to show you what you're missing. What would you have seen if you had done this? And so this is an example. So this is a spider. And it's a special kind of spider. This is called a bola spider. And it doesn't build its webs. What it does is it secretes this sticky stuff off one leg. And when a fly comes around, it does that. And it catches the fly. And then it does what spiders do to flies. But what I want you to see here is look at this thread of fluid that is coming down here. It's not a smooth thing. It's all blobby. It's got what's called this varicosity to it. And this is a manifestation of that really plateau instability, this bobbiness that occurs. If you go out in a morning where there's dew on the ground and you see a spider's web, a regular spider's web, you'll see it's beautiful because it's decorated with these little drops of fluid all along. It originally was the drops were all along this thread. But it didn't like to do that. It wanted to go through the plateau instability and coalesce into these little drops. And so that's, again, something that you've seen. And as I say, it gives texture to the world. OK, so how do we think about this? So we start off with that really plateau instability, but then what happens? And so I'm showing you two pictures here of a drop in the process of breaking apart. And I've hidden everything else about this to you. So you don't see what these are, but I hope you think, yeah, these two things look pretty close to the same thing. They're about the same. So now I want to uncover what I covered up. And so this is what was behind the picture. So let me go back so you can see that this is going to be the drop that's hanging from the top. And this part here is this image that was inverted. So this is actually the top of this thing. And this is that next neck coming out. And you see the same thing here as you saw there. And the point about this, why am I saying this, is, oh, look, what started this? Well, gravity. Gravity was pointing down. In this case, gravity is in this direction. And this is a cone pointing into this sphere. In this case, gravity is up. And the cone is still pointing in the sphere going down. So it didn't care about gravity. Didn't care about the direction of gravity here. That kind of disappeared from the problem. And what I got at the end was this thing which is universal. This thing looks the same, independent of how this drop came away, independent of what the forcing was. And so you can see the images in time. And so we just inverted it. And so this is the argument about how the instability, the shape of the instability, has remained the same, even though everything else has been inverted. And so this is the idea that something here is universal. And so each unhappy drop is unhappy in its own way. And so I have here a bunch of different drops, liquids. So this is the one that you just saw. This is water, falling in air. This is glycerol, something of high viscosity fluid, 1,000 times the viscosity of water, falling in air. And so you see, oh, it's kind of different. It has that thread connecting these two things. Here, this is glycerol on the inside now falling into an outer fluid, which is an oil of the same viscosity as the glycerol. And now that has a cone pointing up and a cone pointing down. So it's a different thing. And here is water falling into a very, very high viscosity fluid. And I don't know if you can still see, but in the back, can you see that there's still a thread of liquid connecting the top to the bottom? Why does nature decide to do it that way? I mean, that is a really strange way for this drop to try and break apart. And so what is it that we do as experimentalists? Well, we get to vary the parameters here. So we can tune ourselves from one kind of behavior to the other. There's what we get to change here, the viscosity of the inner and the outer fluid, the density of the inner outer fluids, the surface tension between them, and the nozzle diameter. And at that point, that's about all that we have to be able to do. OK, so this is what we get to do as experimentalists and tune ourselves into the region of interest for us. And then we try to see what remains that's universal about these drop breaking apart behavior. And so what I want to get across here, so there's one idea which is the most difficult for me to think about or get across originally, which was, well, how do we think about it? And there's this idea that you have this thing called scale invariance. And what is it? So I was at great pains to tell you about that neck in that thread of fluid going to zero. That neck went smaller and smaller and smaller until it no longer had any radius at all. The radius went to zero. That means that that radius was smaller than any other dimension in the problem. It goes to zero. And I'm not talking about the atomic scale because I can't do this doing with optics, or I'm not worried about the atomic scale. So down to one micron, where I can stop visualizing this, this length scale is the only one that matters. It's going to zero. And so the idea is that because the radius is smaller than any other length scale, the dynamics is insensitive to all those other length scales. And so the flow should depend only on that shrinking radius. Now, why would anyone think that? And so what I want you to think about is that you have rain that comes down on a mountain side. And this rain collects into mighty rivers that cross the continent. And then they get to the delta at the mouth of the river. And in the delta, this mighty river breaks up into smaller rivers, streams, brooks, rivulets. And then finally, there's flow between two tiny little pebbles in the stream. And my question to you is, does the flow between those two pebbles depend on the fact that the water originally came from the mountain side? No. Thank you. No, it doesn't make sense. How could we care about that anymore? That kind of information at that very, very different length scale is a waste. It's no longer relevant to the problem. And that's the idea here, is that because this length scale has gotten so much orders of magnitude smaller than any of those other lengths, it doesn't care about them anymore. This is the only length that matters. But then if you say that, then the flow depends only on that shrinking radius. Well, what did that shrinking radius depend on? Well, it depended on the flow. But the flow depended on the radius, which depended on the flow, radius, flow, radius, forward, radius, all the way down. So what I've created for you here is a fractal sentence that I blow up any part of this and I get the original sentence back. And so that's supposed to remind you a bit of what the mathematics of this is. It's a self-similar structure that is appearing in this drop-break-off problem. And if you blow up any part, you regain the original. And so these are the universal shapes that you get because they've got to be self-similar at the point that you begin to break these things apart. So this should remind you a little bit of the behavior that I told you at the beginning of these tree formation where I blow the whole thing up and I get something that looks like the whole tree again. So this is the idea of where some of this universality can come from. So what I want to show, and this is the only picture that's really going to have data on it. And not that I want you to see the data, right? OK, this is. But I want you to know that there is data behind all of these pictures. That is, everything I'm telling you is not just pretty pictures, although I relish the pretty pictures. You have to study these pictures to make sure that you're getting the physics right. And so this is a picture of that. And this equation at the top is that scaling equation that I was trying to tell you was the behavior of this drop breakup. That is, the real radius versus the axial coordinate is the same at different times if I just multiply the radius by some factor and the axial direction by perhaps another factor. And you do that over and over again, and it keeps falling on top of itself. And that's what this picture is supposed to show you, is that as you get closer and closer, you keep getting the same singular shape of this object at that point. OK, so this is the, I could continue telling you lots and lots and lots about drop breakup. But I want to go to the next stage of the drop's life, which is it falls. And if the drop falls, it's going to come down and hit a surface. And if it hits a surface, what does it do? Well, typically, it'll splash. And so what we were interested in is, well, is there anything interesting in the physics of splashing? Again, another thing happens with fluids that are all around us. It's ubiquitous. And so what I want to show you here is a movie of a drop of liquid falling and hitting a plate. What you see here is it's a drop of alcohol. This distance here is about 3 and 1 half millimeters. So it's a small little drop. It's falling from a height, something like this. So it's going to hit this smooth, dry glass microscope, which you can kind of see that gray area there. That's the microscope slide, which is going to hit. So it's going to come down at a meter per second. That's this scale, which is going to occur. And then it's going to splash. And so let's see what that looks like. So it's an ordinary drop. This is what always happens. It's kind of lovely, isn't it? Well, I think so. I'm going to see it again. OK, so watch it. It's going to come down. As soon as it hits, it sees its reflection, it hits. It sends out this corona. And that corona spreads out rapidly and breaks up into lots of little pieces all over the place. And so the question that we want to ask is, well, what creates the splash? So one thing you could ask is, well, clearly, how fast it's falling is going to matter, or how big that drop is. Because if you took a tiny little drop and laid it very carefully on the table, your guess is that it might not splash. It's going to depend on that surface tension, that thing I was telling you about. That's one of the properties of the liquid. That's going to try to hold it together. And it's going to depend on that viscosity, which is how easy it is for this thing to flow on that surface. Those are the properties of the liquid, that of any Newtonian fluid. Those are the things that we end up with. And then there's the surface. The surface is, is it smooth? Is it rough? Is it hard? Is it soft? Is it wet? Is it dry? And now I've kind of run out of properties of what I can talk about with that plate. OK, one thing I didn't tell you about is the air surrounding this. Because the air obviously doesn't matter, right? I mean, I can move my hand back and forth. I don't feel much on it. Air is 1,000 times less dense than the liquid, 1,000 times less dense than the substrate. It can't do much. It gets out of the way. But you do know that if you stick your hand outside the window of a moving car, you feel drag on your hand. It gets pulled back. So what we want to see is, well, how big a splash could we make with this? So if we take this experiment and do this under vacuum, how big a splash could we make? So we want to make the really biggest splash we could. And so what I want to show you is, well, what happens when we do that? And so here is the movie that you'll see for the third time now, so on the left. This is, well, it's an atmospheric pressure. Oh, by the way, I should just point out that that white thing in the middle is just as lit from the back. It's not as if there's any hole in the drop. It's just that that's the lighting of it, how we lit this thing. But it's just an ordinary drop of fluid. And so here it comes. You see it again. You get an ordinary splash coming out. Lovely. And now we do exactly the same experiment over here. So this experiment has the same drop of alcohol. It's the same diameter. It's falling from the same height before it hits this smooth, dry glass microscope slide. And the only thing that's different is it's in a container now in which I remove some of the air. So this is one-third the atmospheric pressure that we have at room temperature, atmospheric pressure in Chicago. So this would be the kind of the air pressure you would get at the top of Mount Everest, one-third of. So you could live in this thing. You wouldn't be happy, but you could live there. That's the, yeah. OK, so the idea here is that we were going to make this very big splash. So I'm going to just show you this splash. So this is the big splash that's going to come. Here it comes. So in the words of Irobi, who ordered that? I mean, this is, I mean, this was a surprise. I mean, we fell down laughing when we saw this. This is hysterical. I mean, it took us a month to stop laughing before we said, OK, now we've got to start doing experiments on this to figure out what's going on. But this is not what you expected. Look, I knew what I've seen this before. So I led you along. But I didn't really do it too badly because this is what we thought was going to happen. What I told you was really what our intuition was was going to happen before we did the experiment. But I want you to feel that intuition, kind of agree with it, and then see that this is just totally bizarre. This is not what you expect. OK, so the air matters. And not only does it matter, it's a control parameter for this problem. And so people have been studying splashing, even with cameras, with photography, since the time of Worthington in 1900. And those images that you created were to die for. So hard to do that with the technology of the time. He was able to get these things. People have studied this, but no one thought to take the air out. Why? Because it's a stupid experiment. I mean, it was not supposed to happen this way. I mean, the other thing, for those of you who know about gases, I mean, you take the air away, and the viscosity doesn't change. I mean, since the viscosity isn't making a difference, how could taking the air away matter? But yet it does. And so the thing that we want to now look at is, well, suppose you go to a higher viscosity fluid. So it's the same thing. Was this only for alcohol? Or is it kind of a generic behavior? And so this is a drop, basically the same kind of experiment. It's just done at 10 times the viscosity of the alcohol, 10 times the viscosity of water. So it's, again, kind of an ordinary drop, just more viscous. And it's at atmospheric pressure. And so I'm going to show you how the thing drops or splashes. Or if it does. So here it comes. It hits. And it just kind of spreads out. And so, well, it's clearly not going to splash. But let's just finish the movie off and see what happens. So I continue this movie. I told you a lie again. It splashes, but with a very different kind of behavior. That is, the morphology of this drop is not the same as the morphology of that alcohol drop that rose up into the air and then broke apart. Here the stuff is just scooting along the surface, almost completely flat. And yet it still is able to break up at the end. And so the question that I wanted to ask here was, well, suppose we take the air away. What happens here? Is it the same thing? And so we go down to 20 kilopascals, so 1 fifth of atmospheric pressure, and do the same experiment with the same liquid. And now you see that this thing, I don't have to stop it to fool you. It just doesn't splash. So this behavior of the splashing and the effective air on splashing is ubiquitous. It depends on, doesn't depend on whether it's viscous or not or how viscous this is. If you take the air away, the splashing stops in this case. So it means you will not get splashing on the moon, no matter how hard you try. You might get it on Mars, but you won't get it on the moon because there's no atmosphere on the moon. OK, so there are lots of things that we could do at this point with this. And so this, again, was a long research project that we worked on to try and figure out what's going on. And one of the things is you can ask, OK, so how does the atomic mass of the gas matter? How does the velocity matter? How does the pressure matter? All of these things and figure out, do scaling on this to try and figure out what's happening. So we did a lot of that. And you could ask the other way of approaching this problem is asking, OK, so where is the air making an effect? So I would have thought, well, maybe underneath. And so we have one student looked at the air underneath the drop and showed, well, that's not doing anything, that the drop just comes down and hits the surface without the air mattering, and it just spreads out and then starts to splash at some much later time. So where the air is mattering is not underneath the drop. So the last thing I want to ask is, well, how about above the drop? And so what I want to show you now is the way we look at what the behavior of the air is doing above the drop. And so we're now going to do a kind of photography which is called Schlieren optics, which is, for those of you don't know, Schlieren optics is a way of being very, very, very sensitive to small changes in the index of refraction of a transparent medium. And so you know what this is kind of when you look at a very hot day on the tarmac of an airplane and you see that you look on the ground and everything looks a little bit wiggly because the air puffs are rising from that hot ground and you see that there's a mirage effect basically that is the stuff is rising. And because of that, things look shimmery. And that's because the index of refraction is a little bit different and your eye is picking that up. And the idea of Schlieren optics is just to magnify that and make that really, really clear. So what I want you to see here is what to look at. So there's this black thing here. That's the drop. That's falling down. That's boring. Don't look at that in this thing. This other black thing is the substrate. Again, that's not to be looked at. That's boring as well. What I want you to look at is the gray area surrounding this drop. And so I'm going to start playing this and then I'm going to stop it just so you can see what it is I want you to look at. And so if I stop it there, you see that you can see the wake of this drop in the air. You see those gray lines coming back up above this behind that drop because it's falling through this region with a changing index refraction. OK, so now I'm going to play the whole movie through. And you can see what you're supposed to look at is that gray area. So let me start this thing off. It hits. So every time a drop is hitting the surface, this is what the air is doing behind it. Now, unfortunately, we analyze this carefully. And this beautiful as these are, this is not what's causing the splash, as far as we can tell. But this is something that happens every single time. And so this is the thing that I hope gives you some comfort tonight when you're in bed and your water tap in your bathroom is dripping and making this noise and keeping you up and getting really frustrated with it. Just think that every time you're hearing that thing pop into the sink, it's creating something like this. And I hope that gives you a little bit of peace as you're trying to fall back to sleep. OK, so this is the end of really what I want to say. That is, what I've been interested in telling you about is the emergence of structure and basically that nature is wondrous. And it renews appreciation of our world when we look at these things. And the other thing is that a lot of these problems have been around for a long time. But the book never closes on a good problem. And so if you look again with renewed interest and renewed tools, you get to see new things emerging. And one of the other things I want to point out as well, there's a certain kind of ideas that I use throughout this talk. And they're basically called scaling or scaling variants, things like this. These are the set of ideas. And they're similar tools and concepts for all these different problems. And that puts me in mind of this quotation from the philosopher Alfred North Whitehead, who said, a great idea, in the case of scaling, the thing that developed over the half century, is a great idea is like a phantom ocean beating upon the shores of human life in successive waves of specialization. And I think that kind of really captures something about what we do as physicists. As we kind of have our set of tools and we can use them over and over again. And each time they come in a little bit differently, but each time something new and beautiful emerges. OK, so that's the end of what I want to tell you about. I really want to also say who are all the people who did the work in here. And so I showed you, of course, Kayi, here working on the Rifts and Rats project. But the people working on that first thing with the fluid instability, viscous fingering, are those on the top row. Michael Brenner, Wendy, Ty, Nathan, Laura, we're all working on the drop breakup problem. And then all of these people on this row are those who worked on the splashing project. And with that, I just want to thank you for your attention. Thank you.