Closing lecture with Anette (Peko) Hosoi
CC Attribution - NonCommercial - NoDerivatives 3.0 Germany:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Hosoi, Anette (Peko)
Professor Anette (Peko) Hosoi has been an Associate Professor of Mechanical Engineering at MIT (Cambridge, US) since 2006. She received her PhD from the University of Chicago in 1997 and first came to MIT as an Applied Mathematics Instructor from 1998 until 2000. She joined the Faculty of Mechanical Engineering in 2002. Hosoi is a specialist in free surface flows, surface tension, and the fluid dynamics of complex fluids. From 2004 until 2006 she was the Doherty Professor in Ocean Utilization. She has won numerous teaching awards, including the Ruth and Joel S. Spira Award for Distinguished Teaching and the Junior Bose Award for Excellence in Teaching. In 2010 MIT selected her to be a MacVicar Fellow.
 Okay, we start with the last session of this conference. It's my great pleasure and honor to introduce Pekka Hosei as plenary speaker. So Pekka got her bachelor in physics in Princeton and then went off to University of Chicago where she got PhD with Leo Karanov and Todd Dupont in 1997 on the subject of suspension. She then went on to become postdoc at Kurrand in New York in the math department. Later she was professor at Ahave-Matt College and since 2002 she is professor at MIT in mechanical engineering and since 2010 also in mathematics. So you see she had been in three different departments, physics, engineering and mathematics. Pekka is famous for her work on free surface flow, swimming, complex fluids, non-Newtonian flow and robotics. She has lots of collaboration with industry. So Wim van Zalos in his talk today puts the scientists in categories and Pekka clearly is a role model for the category of the of Pasteur doing both fundamentals and applications. So Pekka is famous for her inspiring lectures and also for inspiring teaching. She got many teaching awards and she won various awards at the gallery of fluid motion at the APS division of fluid dynamics meeting. She is also famous for a good taste of problems and one of her very recent activities was which I would like to mention is a program which she set up at MIT on sports technology and education at MIT briefly called STEAM. Today she will speak on a subject very broad from biology to robotics. Pekka the floor is yours. Thank you for that fabulous introduction and thank you so much to the organizers for giving me this opportunity and putting together this wonderful meeting. It's been really inspiring and exciting to see all of the work that's going on in the Dutch physics community. So I've really enjoyed the past couple of days. So today I'm going to tell you about biology and robotics and I'm going to start by putting up what might be a controversial quote that appeared in Nature in 2005. So this quote appeared in an essay by William Sutherland and he says, there are increasing calls for biology to be predictive. Optimization is the only approach biology has for making predictions from first principles and the wider adoption of these ideas right across biology should reap ample rewards. So we can argue about the use of the word only in that sentence and I'm in fact going to leave that as an exercise for the audience. So on your train ride home you can debate with your friends whether you can think of other ways for biology to be predictive other than optimization and instead I'm going to focus on this last sentence and tell you about some examples of the rewards that can be had when you apply the tools of optimization to biological systems. And in my group these problems sort of fall into two categories. One is to apply optimization to understand sort of the fundamentals behind the structures and the strategies that we observe in biological systems. So this is really just fundamental science questions. And second is to take that understanding and then apply that to advance engineering design and that's going to be the robotics part that I'll talk about. So I'm going to give examples in both of these categories throughout this talk. So I'm going to start with rationalizing biological structures and strategies in the context of small swimmers. Okay, so small swimmers as you all know small is a relative term so I have to tell you small relative to what. And when you're talking about swimming typically what you'll look at to determine whether something is small is the Reynolds number. So let me remind you just that the Reynolds number is a dimensionless number that quantifies the relative importance of inertial and viscous effects and it's defined as you see up here. So rho is the density of the fluid, mu is the viscosity of the fluid, u is a typical swimming velocity of your swimmer and l is a characteristic size of your swimmer. So now the nice thing about biology is that these swimmers tend to swim in water or they tend to swim in fluids that have material properties that are very close to that of water. Which means that you really can't play with the density or the viscosity. Those are pretty much fixed. So the only way to change the Reynolds number is to change the size of the organism. So let me give you some numbers so you can calibrate yourself so you know what small means in this context. So a person swimming, so if you take a person and throw them into a swimming pool, they tend to swim in a Reynolds number of about 10 to the 5. So now as we go down in scale, if you go down to something about the size of say a duck, ducks are something like a thousand. If you go even smaller you go down to the size of something like an ant. An ant has a Reynolds number of about one. So this is somewhat surprising because in this context that means ants are not yet small. Ants are right at the crossover where viscous and inertial forces are about the same. So we have to go even smaller. So smaller goes around the corner on my plot here. So over here a paramecium, if we go down to the size of a paramecium, that also has a Reynolds number of about one. They're smaller than ants but they're better swimmers so their velocity goes up. Then we go through, there's a few things here that are not motile so they don't swim so we can skip those. The next swimmer that's on the chart is about halfway up. That's the bacterium which is about one micron in size. And the Reynolds number for a bacteria is about 10 to the minus 4. So now we're finally down to something that we can call small. So this is something that is really a low Reynolds number swimmer. And again just to calibrate you, this is sort of roughly the smallest thing that you can see with a light microscope, roughly speaking. So the types of swimmers that I'm going to be interested in are the ones that are sort of between the paramecium and the bacterium on this chart here. So these are going to be single celled organisms or they're going to be bacteria. And so you can imagine if you take a drop of pond water and you put it in a microscope, whatever you see swimming around in there sort of fits into these categories. Okay, so now there's another important thing to take away from this chart which is that if you think about sort of the intuitive way we understand swimming, we do all of this at this scale over here, right, at 10 to the 5. So all of the intuition you've developed about swimming, you've developed a very high Reynolds number. So whatever you've learned over there does not necessarily carry over to this part of the spectrum. And I'm going to show you an example of something to illustrate how our intuition can fail us. Okay, so this is a very famous movie. It was done by G.I. Taylor. So G.I. Taylor is a giant in the field of fluid mechanics. And he made this movie as part of the National Committee for Fluid Mechanics Films. And yes, in the 60s there was a National Committee for Fluid Mechanics Films in the US. And the experiment that Taylor does is the following. So he takes two concentric cylinders, so here's my two concentric cylinders, and in the gap he puts viscous fluid. And then he puts a drop of dye, that red dot there is to represent dye in the fluid, and he's going to slowly turn the inner cylinder to mix the dye in. Okay, so here's the video. So there's the apparatus. It's a very simple apparatus. So here he is inserting the dye. And those of you, maybe you might be able to see the edge of the inner cylinders actually somewhere about here. So it's a very narrow gap. The dye fills the gap about halfway, something like that. Okay, so he puts the drop in. And now he's going to stir it, so he'll take the handle on the top, he'll spin this around. So you can see the drop is now getting mixed in. So he does this, I think he turns it four times or something, that's twice around. So here's three. So far nothing exciting. He's doing exactly what you'd expect. Okay, so, and now for good measures, he's going to turn it the other way to get everything well mixed. So he turns it this way. Okay, you can see sort of the big, you can see the dye is nicely mixed in there. So he's going to go back around, I think twice around this way. And maybe one more time around. And it is now unmixed. Okay, so, and this is real. There's no fakery here. Okay? And if you look at the equations of motion, it's obvious that this has to happen. And the reason this happens is that, so you look at the equations of motion, they balance inertia and viscosity and whatever other physical effects you have in there. If you take inertia out of the equations, time no longer appears explicitly in the equation. So you have some inherent time symmetry in the problem. So everything has to go back. If you take inertia out, everything has to go back to where it started. Okay? And this is a big problem if you are a tiny swimmer, right? Because it means that there are certain things you cannot do if you want to generate some kind of net translation. Okay? So I'm not going to talk about that. There are many, many papers that are written on that. And if you're interested in that, let me just give you this reference. So this is a paper by Purcell called Life at Low Reynolds Number, which appeared in Scientific American. And this was, this is actually a transcript of a lecture that he gave at Harvard. And it's a great introduction to the subject. So he, it's like four pages long. It's very conversational. And I highly recommend it. Okay? So now let me go back to our swimmers. So our swimmers, before I talk about the physics, I have to tell you a little bit about biology. And I am not a biologist. So all of the biology I'm going to tell you I learned in the context of this problem. I just have two slides on biology. The first one I'm going to show you is a fluid-dynamicist's view of biology. Okay? So this is what biology looks like to a fluid-dynamicist. Okay? It's a mess. And it's a terrifying mess. Okay? So this is also a very famous image. So this was done by James Lighthill, who's another great fluid-dynamicist. And so this image came from his paper in Siam Review. This is also another transcript of a lecture that he gave on Flagler hydrodynamics. And there are many things that I love about this picture. First is that it was done in the days before PowerPoint, obviously. And the second one is that he has organized everything in here first and foremost, not by any biological principles, but by how things swim. Okay? So if you look at everything in this center circle here, okay? So everything in the center circle has sort of the same morphology, which means they all have a head, which for this audience, I can approximate as a sphere, and an end-tails, where n is a small number, and that small number is generally one, two, or three. Okay? So everything in this circle basically looks like this guy over here. Okay? Now, the second distinction he draws in here is that he's put prokaryotic cells at the top and eukaryotic cells at the bottom. Okay? And if you think back to your high school biology, you might remember that prokaryotic cells are bacteria, and roughly speaking, eukaryotic cells are everything else. So it's people, it's grasshoppers, it's penguins, it's algae, everything else fits in here. Okay? So this is just bacteria up here, eukaryotic cells down here. Okay? And so this half circle at the top delineates the boundary between those two, so I've colored that line in green. And that boundary happens to be important in the context of this talk because the structure and the mechanics of the tail is very different between prokaryotic and eukaryotic cells. So the cells I'm going to talk about in this talk are in the bottom half, they're the eukaryotic cells, so they're below the green line and within the red circle. Okay? So the second biology slide I have to show you is I have to tell you a little bit about the structure of the tail. Okay? So here, this is what the tail looks like in a eukaryotic cell. Okay? So the tail, it has something that's called a 9 plus 2 microtubule structure. So it basically, if you look at the top diagram here, there are these microtubules that run along the length of the tail and there are nine pairs that go around the outside and then two in the middle. Okay? And one of the remarkable things about this structure is that it is constant across all species. So if you look at the cilia in your lungs, if you look at the flagella on swimming algae, if you look at the sperm on zebras or warthogs or whatever your favorite animal is, all of them have exactly this structure. It's 9 plus 2 microtubule structure, which is remarkably consistent for biology. Okay? So that's the first thing to know and this has two important consequences for this talk. The first is that because the structure is the same, the diameter of all the tails is roughly the same across all species, all species. Okay? So and that diameter is roughly something like 300 nanometers. Okay? So the diameter is a little bit because, you know, it is biology, but it's very close to 300 nanometers. Okay? Second, second, these organisms, so the way they move the tail is they have these microtubules and they can slide them relative to one another like this. So imagine you clamp the microtubules at one end and then you slide them relative to one another further down the tail. That means you're going to induce a local bending moment and the tail will change shape. Okay? So the organism can control the shape of the tail as a function of time. Okay? So now that brings us to our first optimization question and the optimization question is, okay, if I can, oh, thanks. So the optimization question is if I can control the shape of my tail as a function of time, what shape should I choose? Okay? So that's this question here. Can we predict the kinematics observed in microorganisms from purely hydrodynamic considerations? Okay? Okay. So this, I'm not going to show you some work that was done by my graduate student, Daniel Tam, who is now at Delft. So Daniel put together a beautiful model and I'm not going to go into the details of the model, but basically we have the hydrodynamics of the swimmer and there are references here. You can look up how to do it. And the question we want to ask is, please find the optimal curvature as a function of distance along the tail. So what shape should my tail take? Okay? And notice that this is a non-trivial optimization problem because I'm not optimizing one or two parameters. I'm optimizing a shape. So this is a functional optimization that has to be carried out. Okay? But you can do it. It's complicated, but you can do it. And what comes out is this. And this is actually a remarkably, again, a very remarkably robust swimming strategy, no matter what initial conditions we put in, we always get something that looks like this, which looks very much like what you see in biological systems. So you always get a traveling wave. This traveling wave is not a sine wave. It's regions of locally high curvature that are connected by sort of straight segments. So qualitatively, it looks like what you see in biological systems. Quantitatively, it does quite well as well. So the computed optimal ratio of wave amplitude to wavelength is about 0.21. What's measured in this paper over here is 0.2. If I compute number of periods per tail, I get 1.23. What's measured is this one between 1.25 and 1.4. So it seems pretty good. It seems pretty consistent. But in some way, this is not terribly surprising, because if you only have one tail, really, what are you going to do? I mean, that's kind of the only thing you can do with one tail, right? So we thought, okay, well, let's go and think about something that's a little more complicated. What's the next more complicated thing over one tail? Well, it's got to be two tails. Okay, so you put on two tails. So there are many, many microorganisms that have two tails. Actually the most famous one is Clamidomonas, which is this guy up here. So Clamidomonas is a green algae. Biologists love Clamidomonas, and there's lots and lots of data available for it. So we thought, well, since we have so much data, we should try to optimize the strokes that you see in Clamidomonas. And you immediately run into a problem, because it turns out that algae live very rich, fulfilling lives, and there are a lot of things that they're trying to do, right? Because they need to eat, and they need to escape predators, and they need to find other Clamidomonas, and I don't know if they need to communicate with other Clamidomonas, right? So the question is, what are you trying to optimize in this system? It's not at all obvious what the cost function should be. So we decided to take a guess, and we thought, all right, suppose, suppose if I'm an algae, the two most important things to me are to eat and to keep from being eaten. So let's suppose those are the two things that I'm trying to optimize. So here are my goals. You don't have to eat, enhance nutrient uptake, or avoid being eaten, so that's outrun predators, and you don't have to do those at the same time, right? So at some time, you might be doing a stroke that will enhance your nutrient uptake, and at some time, you might be escaping. So here's the answers you get. So if you run the optimization for this to outrun predators, you get these strokes. So these are the two escaping strokes. They look something like that. Actually what Daniel found was four local minima for escaping strokes, but I'm just going to show two here because one of them is, one of them, I'll just show you two here, and I'll tell you in a minute why. Now if I run the optimization for enhancing nutrient uptake, so this is the eating stroke, you get something that looks like this. So it's also very nice, and you can make some pretty movies, so you can put on some, this is what the vorticity field looks like if you compute everything. So like I said, there were four local optima that came out of this and one that came out of this, and out of those five strokes, four are the strokes that are observed in the living clammidomonas. I have a very nice movie here from Ray Goldstein's group of a clammidomonas actually exhibiting three of the four. So this is the clammidomonas here. It's stuck on a pipette. It's currently doing the feeding stroke. And by the way, the feeding stroke is the most common one. So if it's just hanging, the clammidomonas are just hanging out, they do this. So now it's switched over to the escape stroke, and you can trigger this by something called a shock response. So you can shock them with light to get them to go into one of these modes. So now it's gone into the second escape mode. So this is now the anti-symmetric escape mode, and then in a minute it's going to go back and now it's back to its hanging out mode where it's just feeding. So in fact, the optimization routines actually do quite a good job finding the kinematics that you actually see in live organisms. So we thought, OK, that's great. Let's move on to the next question. So what's the next question you might ask? You say, OK, we can get the kinematics quite nicely. What about morphology? Can we predict the shapes in the morphology observed in microorganisms from purely hydrodynamic considerations? And this to me is actually a more interesting question in some way. Because so imagine the following. Imagine someone takes you and throws you into a swimming pool. You're going to flail around, and you're going to select your kinematics until you find something that will allow you to swim. So you can sort of sample a lot of the face space to figure out what is the optimal stroke. Morphology you cannot change. You cannot go into a swimming pool and say, gosh, I'd really like a third arm. I mean, it's not going to happen. So morphology is something that is fixed for you and can only change through evolution. So this question actually gets back to the roots of what is the role of physics and hydrodynamics in evolution. So here's the question we want to ask. So for this problem, we decided to focus on sperm. And the reason we decided to focus on sperm is that they have a very well-defined objective function. They have a packet of genetic material, and they have to move it from one place to another. And that's it. They don't have to eat. They don't have to talk to other sperm. They don't have to do any of that. It's purely transport. So we thought, OK, we have a well-defined objective function. So here's the question we want to ask. If you have a packet of genetic material, which is in the head, so it's packaged in the head here, how big of a motor should I put on that? And the motor is the tail. So how long of a tail should I put on that? And if you think about it a minute, there should be an optimal size, because if your tail is really small, then you're obviously not going to go anywhere. And if your tail is really, really long, then you're expending a lot of energy moving the tail and relatively little moving the head. So there should be some optimal tail length in between. And there is. So here's the plot that Daniel made. So this is basically swimming efficiency. Since there's only two length scales in the problem, the length of the tail and the size of the head, this should really just depend on the ratio of the two, which it does. And I should also say that there is a lot of computation that goes into this plot, because for each one of these points, so let's take this point here. So this point is pick a head size. So here's a head size. Pick a tail size. Here's a tail size. Now, run an optimization for those two guys to find the best possible kinematics and then record the swimming efficiency for those kinematics. So these guys might not be swimming the same way these guys are, but we're allowing everybody to sort of put their best foot forward and swim as best as you possibly can given that morphology. OK? OK, so because otherwise it's not a fair competition. So everybody's swimming the best they possibly can. And this is one of my favorite plots that a student has ever brought to me. And the reason this is one of my favorite plots is because there's an answer. And the answer is 12. It's great. It's 12. OK, so remember the question. The question is how long should the tail be? Well, it should be 12 times the head size. OK? It does all of these other details don't matter. So then the next thing Daniel did is he went into the biology literature and he looked up the morphology of over 400 different mammalian species. So over 400 different mammalian species. And then he made a histogram. OK? So here's what you get from the biological data. It's 12. It's great. So OK, so I was really excited. I was really excited about this. I went and I gave this talk in physics departments and engineering departments and biology departments. And one of the things I learned is that biologists and physicists see something very different in this plot. OK? So physicists and engineers, they tend to look at this and say, oh, this is wonderful. Look, we've learned something fundamental about the way things swim. This is great. And biologists look at this and they say, this is completely boring. Right? The interesting part of this plot is the outliers. Because the outliers are either they are suboptimal, which is kind of unlikely, or they were subject to different evolutionary pressures and constraints, which is now an interesting biology question. OK. So I thought, oh, OK, that sounds good. All right. So I thought, OK, we might as well look at the outliers. So let's take a look at the outliers. OK. So I'm going to show you what one of these outliers are. Before I'm going to give you an exercise. So before I tell you what the answer is, I want you to think of the weirdest mammal you can. OK? So I have 10 seconds to think of the weirdest mammal that you can think of. Now I'm going to tell you the answer. OK. So I give 100% credit to anybody who guessed the bandicoot. I had no idea what a bandicoot was before I did this. OK. Now it turns out that the bandicoot is a marsupial. So I also give partial credit to anybody who guessed marsupials or platypus. Right? But it's still in the same family. OK. So now why does the bandicoot sit out here? OK. So to answer that, I have to go back to a slide I showed you earlier. So one of the slides I showed you earlier is I said this. I said there's this amazing structure, this 9 plus 2 microtubule structure, which has the same diameter across all species. OK. And what I should have said is there's this amazing structure which has the same diameter across all species except for bandicoots. Because there's always an exception in biology. OK. So now why is the bandicoot an exception? So we figured this out because there is in fact a paper that was written in 1958 called the bandicoot spermatozoan and electron microscope study of the tail. OK. So this is known. This is known. Biologists have measured everything. OK. So you go in and here's their electron micrograph. And in fact, it still has the 9 plus 2 microtubule structure. Right? Here's the 9 plus 2 microtubule structure. It sits in here. But it's in this big sheaf. OK. So it's that the radius of the tail is now something like an order of magnitude larger than what you see in the normal tails. OK. And this is a problem because as physicists you know that if your radius goes up, your bending energy goes up enormously. It goes up something like r to the fourth. Right? So there's an enormous bending cost now associated with this that we did not have in our original calculation. And in fact, when you put the bending cost in, what it does is it moves this peak over this way to where the bandicoot sits. And all of these guys down here are animals that have these sort of funny fat tails. OK. So those are those outliers. OK. So those I think we kind of understand. But there's another set of outliers which we do not understand. So I'm just going to tell you what the puzzle is, but I don't have an answer for it. So I'll let you think about what the answer might be. So if you look at this histogram, so the colors on this histogram correspond to different orders. Orders meaning like carnivores or rodents or primates, et cetera, et cetera. And if you take any one of these orders that has a sufficient amount of data in it, they're all sort of centered around 12, just like you think. With the exception of these yellow guys over here. OK. And the yellow guys obviously are not centered around 12. They're centered around something like six. Right? And so they're way off. And in fact, if you look, the swimming efficiency is not, you know, it's at least 50% less if not more than 50% off. So I don't know why they're off. It is statistically significant. We have a lot of species in there. But I can tell you what they are. So the animals that are in this yellow here are something called the even-toed ungulates. OK. And the even-toed ungulates are hooved animals. So they're things like pigs and goats and cows and sheep. OK. And again, like I said, I've given this talk in biology departments. People don't know why these are different. But I think there's an interesting open problem here to understand why that order is fundamentally different. OK. So OK. So that's what I have to say about small swimmers. And now I'm going to shift gears to talk a little bit about robots. OK. So here we go. So now I'm going to talk about bio-inspired design. So bio-inspired design. So this is not a new idea. People have thought about bio-inspired design for many, many years. So here's maybe one of the most famous examples. You guys might recognize this. So this is the burr that inspired the invention of Velcro in 1941. So this guy spent an afternoon picking these out of his dog's fur and thought, wow, this is a really good adhesive and then made Velcro. OK. But of course, bio-inspired design actually has far more failures than it has successes. And if you go onto YouTube, you'll see many, many videos on Flapping Flight, which, as you can tell, is completely ineffective. OK. So the question you have to ask is, OK, if I'm going to do bio-inspired design, what do I do to make? Yeah, I know. I actually really, I love that last part of the movie because he had to be really sure it was going to work before he went off that rock. OK. So the question you have to ask yourself is, how do you ensure that you are in the Velcro, you're making Velcro, and that you're not trying to make this? OK. So we have a couple of basic sort of rules of thumb that we use in my group. So the first is that you should choose a simple organism. OK. So preferably something with a very primitive central nervous system and even more preferably no brain, right? Because I don't want to have to build a brain. I want to do something where the challenges and the solutions lie in the mechanics rather than in the neurological controls, right? So I'm looking for organisms that have mechanical solutions to the challenges. OK. Second, you want to find an organism that is in some way orders of magnitude better than the existing engineering technology. Because if we already have something that does what we want it to do, then why would you go to this complicated biological mechanism, right? So in some way it has to be better. And better is a very, I've deliberately left that as a vague term because it could be an efficiency or robustness or simplicity. There are lots of ways things can be better, but somehow it has to be better than what we already have. And the third and probably most important point on this is that the goal here is not to mimic biology. The goal is to understand the underlying physics of the biological solution and then adopt that in engineering design. OK. So we've applied this to many, many different organisms. And today I'm going to talk about one, which is my most requested organism, which is the snails. OK. So snails. Snails are incredible. So snails, if you take a snail and you put it on the ground, it'll crawl across the ground until it hits a wall and then it'll crawl straight up that wall. And then when it hits the ceiling, it'll flip over and crawl straight across the ceiling. And it doesn't matter if this is grass or dirt or sand or carpet or whatever. It crawls over any kind of substrate you wanted, any angle you want. So wouldn't it be wonderful if we could build a robot that had the same kind of versatility as the snail? OK. So that was our goal. So let's build a robotic snail. OK. So snails, the way they crawl is they secrete a thin film of fluid that sits between the foot and the substrate. OK. And the only way that the foot interacts with the substrate is by generating stresses in this thin film. It never directly touches the substrate. OK. And the way it generates those stresses is by driving waves along the bottom of the foot. So this, I'm going to now show you a movie of a snail crawling up a plate of glass so you can see those waves. And if you find, if you catch a snail, you can put it on a plate of glass and you'll be able to see this. So hopefully you can see. Can you see these waves moving up? OK. So you have waves that are moving up along the bottom of the foot. OK. And if you stare at this for a while, and we've stared at many of these images for a very long time, you start to think, boy, there's something really bizarre looking about this. I mean, other than the obvious fact that you're looking at the bottom of a snail. But there's something very bizarre looking. And the reason it's bizarre is that the waves are going in the wrong direction. Right? So the thing was going to be pushing off the ground. The wave should be going backwards as the thing goes forward. OK. So already there's sort of a puzzle here. OK. So this problem was actually brought to my attention by my graduate student, Brian Chan. So Brian Chan, he got interested in snails. He came to me and said, can I work on the snail project? I said, well, OK. You know, I don't know much about snails. Why don't you go and do a literature search, come back in two weeks, tell me if there's something interesting for us to research, and then we can decide whether or not to look at snails. So Brian said, OK. So he comes back two weeks later, and I said, OK. So what did you find out about snails, Brian? And he said, oh, I solved it. I said, I don't even know what the question was, Brian. What did you solve? So I said, well, Brian, what do you mean you solved it? What did you do? And he said, I built a robot. And I thought, OK. So now you have to understand. This is, I was junior faculty at MIT at the time. Brian was the first PhD student I had ever supervised. And at the time, I had not appreciated that if you give an MIT student a problem with no insufficient constraints, what they do is they build a robot. So Brian built a robot. And it turns out, interestingly, building a robot was exactly the right thing to do in this case. OK. So here's Brian's robot. So this is RoboSnail. So here, I've got these two rigid pieces and these feet that are attached to these rigid pieces. And you activate the robot in the following way. So there's a time series that goes, this is a time series at the top here. And so first you take the rearmost pad and you slide it forward. And then the next one, and you slide it forward, you slide it forward, you slide it forward. And you get this wave of compression that travels along the bottom of the snail. OK. Oh, and I should actually mention, on that movie you saw, on the previous slide with the snail crawling up the glass. The waves that you saw were not out of plane waves. So they are not waves that do this. They are waves of compression that do this. OK. And you can measure that using interferometry or other kinds of tricks. So the thickness of the film actually changes very little. It's the waves you're seeing is something like this. OK. OK. So this is what Brian's snail does. And we can now do the back of the envelope calculation to figure out whether or not this thing will crawl. OK. So here's the model. I'm now going to do just a force balance on this last chunk over here. OK. So the forces that are acting on that chunk are basically the forces that are exerted by the muscle or the motor or whatever you want to say that's pulling this thing forward. And that's resisted by the force that you get from the shear stress in the fluid over here. OK. So now that means this force over here, the muscle force has to be balanced by the shear stress in the fluid. OK. This is, this tau, the shear stress is well known. This is something called couette flow in a small gap. And we know that the shear stress is inversely proportional to the gap thickness and linearly proportional to the velocity at which you move the top plate and to the viscosity of this fluid. OK. You do the same force balance on this other chunk. And then you just say that the velocity of the center of mass of snail is the average velocity of all of the feet. And you come out with an answer. And it takes three lines or something. You can do it on a napkin. And you get the following. So the velocity of the snail looks like this. And there are a couple of interesting things about this calculation. So first there's this nice pre-factor. But the most important part is this guy over here. So this says that the snail velocity is proportional to one over the viscosity that pad 1 sees minus one over the viscosity that the rest of this guy sees. OK. Now, so what does that mean? That means if I have a fluid with a constant viscosity, this thing cannot move. So it just sits there and does this. Right? So it's basically, I mean, this is treadmilling or something. It's jogging in place. OK. So it does that. OK. Now, however, as soon as I have any kind of non-linearity in the viscosity, so if I have anything like if the viscosity in some way depends on the local shear stress or the local shear rate, or I put in anything that deviates from a constant, the thing will crawl. OK. So the type of non-linearity I put in determines the direction it goes. Right? Because there's a minus sign here. Right? So I can flip the sign on this by flipping these around. So if I have something called a shear thickening fluid in which my viscosity increases as the shear stress increases, then the wave goes in the same direction that the snail is crawling. If I have something called a shear thinning fluid, so the viscosity decreases as the shear stress goes up, then the wave goes in the opposite direction to the way the snail is crawling. In fact, if you go and look at snails, they exhibit both types of behavior. Land snails, which have very shear thickening mucus, have waves that go in the same direction that the snail is crawling. And we know that land snails, mucus has this property because there is a PhD thesis by Mark Denney that was published in Nature in 1980 on the rheological properties of snail slime. Mark Denney, when I talked to him, had no idea anybody would ever cite that paper, but it's turned out to be incredibly important. Okay, so now the last thing I'll show you is, of course, the RoboSnail climbing. It's a snail, so it's very slow, but so this is a movie of RoboSnail climbing up a glass plate. So we had no snail slime in the lab, so we used whatever we had because, like you saw on the previous slide, we could use any kind of fluid that has this nice non-Newtonian property. Okay? It climbs upside down on ceilings. It's actually easier to go on ceilings than to go up walls, right, because up walls, you're fighting gravity both in this direction and gravity is trying to pull you off the wall, but on ceilings, gravity is just trying to pull you up the wall, but it's not impeding your progress, right? So this is actually the easier thing. And it's running now on carbapole, which is the, it's a commercial product that they put in hair gel, so it's just a fluid that has a yield stress to it. Okay, so, and now let me put up just the most important slide, I think, which is these are the people who actually did the work. So first, Daniel Tam, who did all the work on the small swimmers and is currently an assistant professor in Delft, so he's one of the locals now. Brian Shan, who is currently staff at MIT, so he's the guy who actually built the robot. And Randy Hewald, I wanted to throw up there, even though I didn't talk very much about the rheology of snail slime, he did a tremendous amount on the rheology of snail slime, which helped us to optimize the snail as far as crawling. And then I talked to many, many, many, many biologists who taught me a lot of biology, particularly the most important ones, Linda Turner at Harvard and Suisd Swar is at Cornell. And I would like to thank you for your attention. Thank you, Begu, for this wonderful talk. So if possible, I would like to take some questions. It's hard to see questions. Well, there's some question over there. Do we have a mic or should we shout? Well, I was wondering, when you did the simulation on the tail, it was all moving pretty in place. Oh, yeah. And I guess in the real world, they're not, but the results seem to be the same. Yes, good. That's a great question. So the question was, in our simulations, all of the motions of the tail seem to be in plane, whereas the real world is obviously 3D, so things can in fact move in other directions. So absolutely, so typically speaking, and in fact, let me just go back to this one slide. So if you look at the microtubule arrangement, let me go back to this here, you notice that the symmetry is actually broken in this tail. Oh, my talk is gone. Okay, never mind. Okay, so remember, there are two microtubules in the center, which break the symmetry of the tail. So the tail actually prefers to bend in a plane. Now, having said that, there are lots of organisms that actually swim using, bending their tail in a spiral. There it is. So you see here, right here, the symmetry is broken, so it tends to like to bend along that other axis. So most of the swimmers of the data that we looked at, they actually do bend the tail in a plane, which is not, again, it's biology. So there are always exceptions, and I think the ones that actually use the spiral are very efficient swimmers. Oh, yes? Yeah. Has Robosnil had any practical applications? Oh, good question. So the question is, has Robosnil had any practical applications? And the answer is yes. So that research was actually funded by Schlumberger, and Schlumberger was interested in developing crawlers for their downhole drilling environments. So when you drill a hole for oil recovery, you basically, you send down a slurry, and you sort of grind up whatever's down there, and then you have to pump everything back out, which means that you have a tube that is full of something called drilling mud. And this drilling mud is a very non-Newtonian fluid. It has a yield stress. It's sticky stuff. And the problem is that if you send a robot down and it gets stuck, you're done. You have to drill another hole. There's nothing you can do to get it out. So what they wanted was they wanted a robot that would not get stuck. And Robosnil is designed to crawl on exactly that kind of fluid. So the stickier and gummier, the better, right? Because it's closer to snail slime. So after we published this, we passed that on to Schlumberger, who are now developing those ideas into crawlers for their downhole environments. Thank you once more for a wonderful talk.
 Okay, we start with the last session of this conference.  It's my great pleasure and honor to introduce Pekka Hosei as plenary speaker.  So Pekka got her bachelor in physics in Princeton and then went off to University of Chicago  where she got PhD with Leo Karanov and Todd Dupont in 1997 on the subject of suspension.  She then went on to become postdoc at Kurrand in New York in the math department.  Later she was professor at Ahave-Matt College and since 2002 she is professor at MIT in  mechanical engineering and since 2010 also in mathematics.  So you see she had been in three different departments, physics, engineering and mathematics.  Pekka is famous for her work on free surface flow, swimming, complex fluids, non-Newtonian  flow and robotics.  She has lots of collaboration with industry.  So Wim van Zalos in his talk today puts the scientists in categories and Pekka clearly  is a role model for the category of the of Pasteur doing both fundamentals and applications.  So Pekka is famous for her inspiring lectures and also for inspiring teaching.  She got many teaching awards and she won various awards at the gallery of fluid motion at the  APS division of fluid dynamics meeting.  She is also famous for a good taste of problems and one of her very recent activities was  which I would like to mention is a program which she set up at MIT on sports technology  and education at MIT briefly called STEAM.  Today she will speak on a subject very broad from biology to robotics.  Pekka the floor is yours.  Thank you for that fabulous introduction and thank you so much to the organizers for giving  me this opportunity and putting together this wonderful meeting.  It's been really inspiring and exciting to see all of the work that's going on in the  Dutch physics community.  So I've really enjoyed the past couple of days.  So today I'm going to tell you about biology and robotics and I'm going to start by putting  up what might be a controversial quote that appeared in Nature in 2005.  So this quote appeared in an essay by William Sutherland and he says, there are increasing  calls for biology to be predictive.  Optimization is the only approach biology has for making predictions from first principles  and the wider adoption of these ideas right across biology should reap ample rewards.  So we can argue about the use of the word only in that sentence and I'm in fact going  to leave that as an exercise for the audience.  So on your train ride home you can debate with your friends whether you can think of  other ways for biology to be predictive other than optimization and instead I'm going to  focus on this last sentence and tell you about some examples of the rewards that can be had  when you apply the tools of optimization to biological systems.  And in my group these problems sort of fall into two categories.  One is to apply optimization to understand sort of the fundamentals behind the structures  and the strategies that we observe in biological systems.  So this is really just fundamental science questions.  And second is to take that understanding and then apply that to advance engineering design  and that's going to be the robotics part that I'll talk about.  So I'm going to give examples in both of these categories throughout this talk.  So I'm going to start with rationalizing biological structures and strategies in the  context of small swimmers.  Okay, so small swimmers as you all know small is a relative term so I have to tell you small  relative to what.  And when you're talking about swimming typically what you'll look at to determine whether something  is small is the Reynolds number.  So let me remind you just that the Reynolds number is a dimensionless number that quantifies  the relative importance of inertial and viscous effects and it's defined as you see up here.  So rho is the density of the fluid, mu is the viscosity of the fluid, u is a typical swimming  velocity of your swimmer and l is a characteristic size of your swimmer.  So now the nice thing about biology is that these swimmers tend to swim in water or they  tend to swim in fluids that have material properties that are very close to that of water.  Which means that you really can't play with the density or the viscosity.  Those are pretty much fixed.  So the only way to change the Reynolds number is to change the size of the organism.  So let me give you some numbers so you can calibrate yourself so you know what small  means in this context.  So a person swimming, so if you take a person and throw them into a swimming pool, they  tend to swim in a Reynolds number of about 10 to the 5.  So now as we go down in scale, if you go down to something about the size of say a duck,  ducks are something like a thousand.  If you go even smaller you go down to the size of something like an ant.  An ant has a Reynolds number of about one.  So this is somewhat surprising because in this context that means ants are not yet small.  Ants are right at the crossover where viscous and inertial forces are about the same.  So we have to go even smaller.  So smaller goes around the corner on my plot here.  So over here a paramecium, if we go down to the size of a paramecium, that also has a  Reynolds number of about one.  They're smaller than ants but they're better swimmers so their velocity goes up.  Then we go through, there's a few things here that are not motile so they don't swim  so we can skip those.  The next swimmer that's on the chart is about halfway up.  That's the bacterium which is about one micron in size.  And the Reynolds number for a bacteria is about 10 to the minus 4.  So now we're finally down to something that we can call small.  So this is something that is really a low Reynolds number swimmer.  And again just to calibrate you, this is sort of roughly the smallest thing that you can  see with a light microscope, roughly speaking.  So the types of swimmers that I'm going to be interested in are the ones that are sort  of between the paramecium and the bacterium on this chart here.  So these are going to be single celled organisms or they're going to be bacteria.  And so you can imagine if you take a drop of pond water and you put it in a microscope,  whatever you see swimming around in there sort of fits into these categories.  Okay, so now there's another important thing to take away from this chart which is that  if you think about sort of the intuitive way we understand swimming, we do all of this  at this scale over here, right, at 10 to the 5.  So all of the intuition you've developed about swimming, you've developed a very high  Reynolds number.  So whatever you've learned over there does not necessarily carry over to this part of  the spectrum.  And I'm going to show you an example of something to illustrate how our intuition can fail us.  Okay, so this is a very famous movie.  It was done by G.I.  Taylor.  So G.I.  Taylor is a giant in the field of fluid mechanics.  And he made this movie as part of the National Committee for Fluid Mechanics Films.  And yes, in the 60s there was a National Committee for Fluid Mechanics Films in the US.  And the experiment that Taylor does is the following.  So he takes two concentric cylinders, so here's my two concentric cylinders, and in  the gap he puts viscous fluid.  And then he puts a drop of dye, that red dot there is to represent dye in the fluid, and  he's going to slowly turn the inner cylinder to mix the dye in.  Okay, so here's the video.  So there's the apparatus.  It's a very simple apparatus.  So here he is inserting the dye.  And those of you, maybe you might be able to see the edge of the inner cylinders actually  somewhere about here.  So it's a very narrow gap.  The dye fills the gap about halfway, something like that.  Okay, so he puts the drop in.  And now he's going to stir it, so he'll take the handle on the top, he'll spin this around.  So you can see the drop is now getting mixed in.  So he does this, I think he turns it four times or something, that's twice around.  So here's three.  So far nothing exciting.  He's doing exactly what you'd expect.  Okay, so, and now for good measures, he's going to turn it the other way to get everything  well mixed.  So he turns it this way.  Okay, you can see sort of the big, you can see the dye is nicely mixed in there.  So he's going to go back around, I think twice around this way.  And maybe one more time around.  And it is now unmixed.  Okay, so, and this is real.  There's no fakery here.  Okay?  And if you look at the equations of motion, it's obvious that this has to happen.  And the reason this happens is that, so you look at the equations of motion, they balance  inertia and viscosity and whatever other physical effects you have in there.  If you take inertia out of the equations, time no longer appears explicitly in the equation.  So you have some inherent time symmetry in the problem.  So everything has to go back.  If you take inertia out, everything has to go back to where it started.  Okay?  And this is a big problem if you are a tiny swimmer, right?  Because it means that there are certain things you cannot do if you want to generate some  kind of net translation.  Okay?  So I'm not going to talk about that.  There are many, many papers that are written on that.  And if you're interested in that, let me just give you this reference.  So this is a paper by Purcell called Life at Low Reynolds Number, which appeared in Scientific  American.  And this was, this is actually a transcript of a lecture that he gave at Harvard.  And it's a great introduction to the subject.  So he, it's like four pages long.  It's very conversational.  And I highly recommend it.  Okay?  So now let me go back to our swimmers.  So our swimmers, before I talk about the physics, I have to tell you a little bit about biology.  And I am not a biologist.  So all of the biology I'm going to tell you I learned in the context of this problem.  I just have two slides on biology.  The first one I'm going to show you is a fluid-dynamicist's view of biology.  Okay?  So this is what biology looks like to a fluid-dynamicist.  Okay?  It's a mess.  And it's a terrifying mess.  Okay?  So this is also a very famous image.  So this was done by James Lighthill, who's another great fluid-dynamicist.  And so this image came from his paper in Siam Review.  This is also another transcript of a lecture that he gave on Flagler hydrodynamics.  And there are many things that I love about this picture.  First is that it was done in the days before PowerPoint, obviously.  And the second one is that he has organized everything in here first and foremost, not  by any biological principles, but by how things swim.  Okay?  So if you look at everything in this center circle here, okay?  So everything in the center circle has sort of the same morphology, which means they all  have a head, which for this audience, I can approximate as a sphere, and an end-tails,  where n is a small number, and that small number is generally one, two, or three.  Okay?  So everything in this circle basically looks like this guy over here.  Okay?  Now, the second distinction he draws in here is that he's put prokaryotic cells at the  top and eukaryotic cells at the bottom.  Okay?  And if you think back to your high school biology, you might remember that prokaryotic  cells are bacteria, and roughly speaking, eukaryotic cells are everything else.  So it's people, it's grasshoppers, it's penguins, it's algae, everything else fits in here.  Okay?  So this is just bacteria up here, eukaryotic cells down here.  Okay?  And so this half circle at the top delineates the boundary between those two, so I've colored  that line in green.  And that boundary happens to be important in the context of this talk because the structure  and the mechanics of the tail is very different between prokaryotic and eukaryotic cells.  So the cells I'm going to talk about in this talk are in the bottom half, they're the eukaryotic  cells, so they're below the green line and within the red circle.  Okay?  So the second biology slide I have to show you is I have to tell you a little bit about  the structure of the tail.  Okay?  So here, this is what the tail looks like in a eukaryotic cell.  Okay?  So the tail, it has something that's called a 9 plus 2 microtubule structure.  So it basically, if you look at the top diagram here, there are these microtubules that run  along the length of the tail and there are nine pairs that go around the outside and  then two in the middle.  Okay?  And one of the remarkable things about this structure is that it is constant across all  species.  So if you look at the cilia in your lungs, if you look at the flagella on swimming algae,  if you look at the sperm on zebras or warthogs or whatever your favorite animal is, all of  them have exactly this structure.  It's 9 plus 2 microtubule structure, which is remarkably consistent for biology.  Okay?  So that's the first thing to know and this has two important consequences for this talk.  The first is that because the structure is the same, the diameter of all the tails is  roughly the same across all species, all species.  Okay?  So and that diameter is roughly something like 300 nanometers.  Okay?  So the diameter is a little bit because, you know, it is biology, but it's very close  to 300 nanometers.  Okay?  Second, second, these organisms, so the way they move the tail is they have these microtubules  and they can slide them relative to one another like this.  So imagine you clamp the microtubules at one end and then you slide them relative to one  another further down the tail.  That means you're going to induce a local bending moment and the tail will change shape.  Okay?  So the organism can control the shape of the tail as a function of time.  Okay?  So now that brings us to our first optimization question and the optimization question is,  okay, if I can, oh, thanks.  So the optimization question is if I can control the shape of my tail as a function of time,  what shape should I choose?  Okay?  So that's this question here.  Can we predict the kinematics observed in microorganisms from purely hydrodynamic considerations?  Okay?  Okay.  So this, I'm not going to show you some work that was done by my graduate student, Daniel  Tam, who is now at Delft.  So Daniel put together a beautiful model and I'm not going to go into the details of the  model, but basically we have the hydrodynamics of the swimmer and there are references here.  You can look up how to do it.  And the question we want to ask is, please find the optimal curvature as a function  of distance along the tail.  So what shape should my tail take?  Okay?  And notice that this is a non-trivial optimization problem because I'm not optimizing one or  two parameters.  I'm optimizing a shape.  So this is a functional optimization that has to be carried out.  Okay?  But you can do it.  It's complicated, but you can do it.  And what comes out is this.  And this is actually a remarkably, again, a very remarkably robust swimming strategy,  no matter what initial conditions we put in, we always get something that looks like this,  which looks very much like what you see in biological systems.  So you always get a traveling wave.  This traveling wave is not a sine wave.  It's regions of locally high curvature that are connected by sort of straight segments.  So qualitatively, it looks like what you see in biological systems.  Quantitatively, it does quite well as well.  So the computed optimal ratio of wave amplitude to wavelength is about 0.21.  What's measured in this paper over here is 0.2.  If I compute number of periods per tail, I get 1.23.  What's measured is this one between 1.25 and 1.4.  So it seems pretty good.  It seems pretty consistent.  But in some way, this is not terribly surprising, because if you only have one tail, really,  what are you going to do?  I mean, that's kind of the only thing you can do with one tail, right?  So we thought, okay, well, let's go and think about something that's a little more complicated.  What's the next more complicated thing over one tail?  Well, it's got to be two tails.  Okay, so you put on two tails.  So there are many, many microorganisms that have two tails.  Actually the most famous one is Clamidomonas, which is this guy up here.  So Clamidomonas is a green algae.  Biologists love Clamidomonas, and there's lots and lots of data available for it.  So we thought, well, since we have so much data, we should try to optimize the strokes  that you see in Clamidomonas.  And you immediately run into a problem, because it turns out that algae live very rich, fulfilling  lives, and there are a lot of things that they're trying to do, right?  Because they need to eat, and they need to escape predators, and they need to find other  Clamidomonas, and I don't know if they need to communicate with other Clamidomonas, right?  So the question is, what are you trying to optimize in this system?  It's not at all obvious what the cost function should be.  So we decided to take a guess, and we thought, all right, suppose, suppose if I'm an algae,  the two most important things to me are to eat and to keep from being eaten.  So let's suppose those are the two things that I'm trying to optimize.  So here are my goals.  You don't have to eat, enhance nutrient uptake, or avoid being eaten, so that's outrun predators,  and you don't have to do those at the same time, right?  So at some time, you might be doing a stroke that will enhance your nutrient uptake, and  at some time, you might be escaping.  So here's the answers you get.  So if you run the optimization for this to outrun predators, you get these strokes.  So these are the two escaping strokes.  They look something like that.  Actually what Daniel found was four local minima for escaping strokes, but I'm just going  to show two here because one of them is, one of them, I'll just show you two here, and  I'll tell you in a minute why.  Now if I run the optimization for enhancing nutrient uptake, so this is the eating stroke,  you get something that looks like this.  So it's also very nice, and you can make some pretty movies, so you can put on some,  this is what the vorticity field looks like if you compute everything.  So like I said, there were four local optima that came out of this and one that came out  of this, and out of those five strokes, four are the strokes that are observed in the living  clammidomonas.  I have a very nice movie here from Ray Goldstein's group of a clammidomonas actually exhibiting  three of the four.  So this is the clammidomonas here.  It's stuck on a pipette.  It's currently doing the feeding stroke.  And by the way, the feeding stroke is the most common one.  So if it's just hanging, the clammidomonas are just hanging out, they do this.  So now it's switched over to the escape stroke, and you can trigger this by something called  a shock response.  So you can shock them with light to get them to go into one of these modes.  So now it's gone into the second escape mode.  So this is now the anti-symmetric escape mode, and then in a minute it's going to go back  and now it's back to its hanging out mode where it's just feeding.  So in fact, the optimization routines actually do quite a good job finding the kinematics  that you actually see in live organisms.  So we thought, OK, that's great.  Let's move on to the next question.  So what's the next question you might ask?  You say, OK, we can get the kinematics quite nicely.  What about morphology?  Can we predict the shapes in the morphology observed in microorganisms from purely hydrodynamic  considerations?  And this to me is actually a more interesting question in some way.  Because so imagine the following.  Imagine someone takes you and throws you into a swimming pool.  You're going to flail around, and you're going to select your kinematics until you find something  that will allow you to swim.  So you can sort of sample a lot of the face space to figure out what is the optimal stroke.  Morphology you cannot change.  You cannot go into a swimming pool and say, gosh, I'd really like a third arm.  I mean, it's not going to happen.  So morphology is something that is fixed for you and can only change through evolution.  So this question actually gets back to the roots of what is the role of physics and hydrodynamics  in evolution.  So here's the question we want to ask.  So for this problem, we decided to focus on sperm.  And the reason we decided to focus on sperm is that they have a very well-defined objective  function.  They have a packet of genetic material, and they have to move it from one place to another.  And that's it.  They don't have to eat.  They don't have to talk to other sperm.  They don't have to do any of that.  It's purely transport.  So we thought, OK, we have a well-defined objective function.  So here's the question we want to ask.  If you have a packet of genetic material, which is in the head, so it's packaged in  the head here, how big of a motor should I put on that?  And the motor is the tail.  So how long of a tail should I put on that?  And if you think about it a minute, there should be an optimal size, because if your  tail is really small, then you're obviously not going to go anywhere.  And if your tail is really, really long, then you're expending a lot of energy moving the  tail and relatively little moving the head.  So there should be some optimal tail length in between.  And there is.  So here's the plot that Daniel made.  So this is basically swimming efficiency.  Since there's only two length scales in the problem, the length of the tail and the size  of the head, this should really just depend on the ratio of the two, which it does.  And I should also say that there is a lot of computation that goes into this plot, because  for each one of these points, so let's take this point here.  So this point is pick a head size.  So here's a head size.  Pick a tail size.  Here's a tail size.  Now, run an optimization for those two guys to find the best possible kinematics and then  record the swimming efficiency for those kinematics.  So these guys might not be swimming the same way these guys are, but we're allowing everybody  to sort of put their best foot forward and swim as best as you possibly can given that  morphology.  OK?  OK, so because otherwise it's not a fair competition.  So everybody's swimming the best they possibly can.  And this is one of my favorite plots that a student has ever brought to me.  And the reason this is one of my favorite plots is because there's an answer.  And the answer is 12.  It's great.  It's 12.  OK, so remember the question.  The question is how long should the tail be?  Well, it should be 12 times the head size.  OK?  It does all of these other details don't matter.  So then the next thing Daniel did is he went into the biology literature and he looked  up the morphology of over 400 different mammalian species.  So over 400 different mammalian species.  And then he made a histogram.  OK?  So here's what you get from the biological data.  It's 12.  It's great.  So OK, so I was really excited.  I was really excited about this.  I went and I gave this talk in physics departments and engineering departments and biology departments.  And one of the things I learned is that biologists and physicists see something very different  in this plot.  OK?  So physicists and engineers, they tend to look at this and say, oh, this is wonderful.  Look, we've learned something fundamental about the way things swim.  This is great.  And biologists look at this and they say, this is completely boring.  Right?  The interesting part of this plot is the outliers.  Because the outliers are either they are suboptimal, which is kind of unlikely, or they were subject  to different evolutionary pressures and constraints, which is now an interesting biology question.  OK.  So I thought, oh, OK, that sounds good.  All right.  So I thought, OK, we might as well look at the outliers.  So let's take a look at the outliers.  OK.  So I'm going to show you what one of these outliers are.  Before I'm going to give you an exercise.  So before I tell you what the answer is, I want you to think of the weirdest mammal you  can.  OK?  So I have 10 seconds to think of the weirdest mammal that you can think of.  Now I'm going to tell you the answer.  OK.  So I give 100% credit to anybody who guessed the bandicoot.  I had no idea what a bandicoot was before I did this.  OK.  Now it turns out that the bandicoot is a marsupial.  So I also give partial credit to anybody who guessed marsupials or platypus.  Right?  But it's still in the same family.  OK.  So now why does the bandicoot sit out here?  OK.  So to answer that, I have to go back to a slide I showed you earlier.  So one of the slides I showed you earlier is I said this.  I said there's this amazing structure, this 9 plus 2 microtubule structure, which has  the same diameter across all species.  OK.  And what I should have said is there's this amazing structure which has the same diameter  across all species except for bandicoots.  Because there's always an exception in biology.  OK.  So now why is the bandicoot an exception?  So we figured this out because there is in fact a paper that was written in 1958 called  the bandicoot spermatozoan and electron microscope study of the tail.  OK.  So this is known.  This is known.  Biologists have measured everything.  OK.  So you go in and here's their electron micrograph.  And in fact, it still has the 9 plus 2 microtubule structure.  Right?  Here's the 9 plus 2 microtubule structure.  It sits in here.  But it's in this big sheaf.  OK.  So it's that the radius of the tail is now something like an order of magnitude larger  than what you see in the normal tails.  OK.  And this is a problem because as physicists you know that if your radius goes up, your  bending energy goes up enormously.  It goes up something like r to the fourth.  Right?  So there's an enormous bending cost now associated with this that we did not have in our original  calculation.  And in fact, when you put the bending cost in, what it does is it moves this peak over  this way to where the bandicoot sits.  And all of these guys down here are animals that have these sort of funny fat tails.  OK.  So those are those outliers.  OK.  So those I think we kind of understand.  But there's another set of outliers which we do not understand.  So I'm just going to tell you what the puzzle is, but I don't have an answer for it.  So I'll let you think about what the answer might be.  So if you look at this histogram, so the colors on this histogram correspond to different  orders.  Orders meaning like carnivores or rodents or primates, et cetera, et cetera.  And if you take any one of these orders that has a sufficient amount of data in it, they're  all sort of centered around 12, just like you think.  With the exception of these yellow guys over here.  OK.  And the yellow guys obviously are not centered around 12.  They're centered around something like six.  Right?  And so they're way off.  And in fact, if you look, the swimming efficiency is not, you know, it's at least 50% less if  not more than 50% off.  So I don't know why they're off.  It is statistically significant.  We have a lot of species in there.  But I can tell you what they are.  So the animals that are in this yellow here are something called the even-toed ungulates.  OK.  And the even-toed ungulates are hooved animals.  So they're things like pigs and goats and cows and sheep.  OK.  And again, like I said, I've given this talk in biology departments.  People don't know why these are different.  But I think there's an interesting open problem here to understand why that order is fundamentally  different.  OK.  So OK.  So that's what I have to say about small swimmers.  And now I'm going to shift gears to talk a little bit about robots.  OK.  So here we go.  So now I'm going to talk about bio-inspired design.  So bio-inspired design.  So this is not a new idea.  People have thought about bio-inspired design for many, many years.  So here's maybe one of the most famous examples.  You guys might recognize this.  So this is the burr that inspired the invention of Velcro in 1941.  So this guy spent an afternoon picking these out of his dog's fur and thought, wow, this  is a really good adhesive and then made Velcro.  OK.  But of course, bio-inspired design actually has far more failures than it has successes.  And if you go onto YouTube, you'll see many, many videos on Flapping Flight, which, as  you can tell, is completely ineffective.  OK.  So the question you have to ask is, OK, if I'm going to do bio-inspired design, what  do I do to make?  Yeah, I know.  I actually really, I love that last part of the movie because he had to be really sure  it was going to work before he went off that rock.  OK.  So the question you have to ask yourself is, how do you ensure that you are in the Velcro,  you're making Velcro, and that you're not trying to make this?  OK.  So we have a couple of basic sort of rules of thumb that we use in my group.  So the first is that you should choose a simple organism.  OK.  So preferably something with a very primitive central nervous system and even more preferably  no brain, right?  Because I don't want to have to build a brain.  I want to do something where the challenges and the solutions lie in the mechanics rather  than in the neurological controls, right?  So I'm looking for organisms that have mechanical solutions to the challenges.  OK.  Second, you want to find an organism that is in some way orders of magnitude better  than the existing engineering technology.  Because if we already have something that does what we want it to do, then why would  you go to this complicated biological mechanism, right?  So in some way it has to be better.  And better is a very, I've deliberately left that as a vague term because it could be an  efficiency or robustness or simplicity.  There are lots of ways things can be better, but somehow it has to be better than what  we already have.  And the third and probably most important point on this is that the goal here is not  to mimic biology.  The goal is to understand the underlying physics of the biological solution and then adopt  that in engineering design.  OK.  So we've applied this to many, many different organisms.  And today I'm going to talk about one, which is my most requested organism, which is the  snails.  OK.  So snails.  Snails are incredible.  So snails, if you take a snail and you put it on the ground, it'll crawl across the ground  until it hits a wall and then it'll crawl straight up that wall.  And then when it hits the ceiling, it'll flip over and crawl straight across the ceiling.  And it doesn't matter if this is grass or dirt or sand or carpet or whatever.  It crawls over any kind of substrate you wanted, any angle you want.  So wouldn't it be wonderful if we could build a robot that had the same kind of versatility  as the snail?  OK.  So that was our goal.  So let's build a robotic snail.  OK.  So snails, the way they crawl is they secrete a thin film of fluid that sits between the  foot and the substrate.  OK.  And the only way that the foot interacts with the substrate is by generating stresses  in this thin film.  It never directly touches the substrate.  OK.  And the way it generates those stresses is by driving waves along the bottom of the foot.  So this, I'm going to now show you a movie of a snail crawling up a plate of glass so  you can see those waves.  And if you find, if you catch a snail, you can put it on a plate of glass and you'll  be able to see this.  So hopefully you can see.  Can you see these waves moving up?  OK.  So you have waves that are moving up along the bottom of the foot.  OK.  And if you stare at this for a while, and we've stared at many of these images for a very  long time, you start to think, boy, there's something really bizarre looking about this.  I mean, other than the obvious fact that you're looking at the bottom of a snail.  But there's something very bizarre looking.  And the reason it's bizarre is that the waves are going in the wrong direction.  Right?  So the thing was going to be pushing off the ground.  The wave should be going backwards as the thing goes forward.  OK.  So already there's sort of a puzzle here.  OK.  So this problem was actually brought to my attention by my graduate student, Brian Chan.  So Brian Chan, he got interested in snails.  He came to me and said, can I work on the snail project?  I said, well, OK.  You know, I don't know much about snails.  Why don't you go and do a literature search, come back in two weeks, tell me if there's  something interesting for us to research, and then we can decide whether or not to look  at snails.  So Brian said, OK.  So he comes back two weeks later, and I said, OK.  So what did you find out about snails, Brian?  And he said, oh, I solved it.  I said, I don't even know what the question was, Brian.  What did you solve?  So I said, well, Brian, what do you mean you solved it?  What did you do?  And he said, I built a robot.  And I thought, OK.  So now you have to understand.  This is, I was junior faculty at MIT at the time.  Brian was the first PhD student I had ever supervised.  And at the time, I had not appreciated that if you give an MIT student a problem with  no insufficient constraints, what they do is they build a robot.  So Brian built a robot.  And it turns out, interestingly, building a robot was exactly the right thing to do  in this case.  OK.  So here's Brian's robot.  So this is RoboSnail.  So here, I've got these two rigid pieces and these feet that are attached to these rigid  pieces.  And you activate the robot in the following way.  So there's a time series that goes, this is a time series at the top here.  And so first you take the rearmost pad and you slide it forward.  And then the next one, and you slide it forward, you slide it forward, you slide it forward.  And you get this wave of compression that travels along the bottom of the snail.  OK.  Oh, and I should actually mention, on that movie you saw, on the previous slide with  the snail crawling up the glass.  The waves that you saw were not out of plane waves.  So they are not waves that do this.  They are waves of compression that do this.  OK.  And you can measure that using interferometry or other kinds of tricks.  So the thickness of the film actually changes very little.  It's the waves you're seeing is something like this.  OK.  OK.  So this is what Brian's snail does.  And we can now do the back of the envelope calculation to figure out whether or not this  thing will crawl.  OK.  So here's the model.  I'm now going to do just a force balance on this last chunk over here.  OK.  So the forces that are acting on that chunk are basically the forces that are exerted  by the muscle or the motor or whatever you want to say that's pulling this thing forward.  And that's resisted by the force that you get from the shear stress in the fluid over  here.  OK.  So now that means this force over here, the muscle force has to be balanced by the  shear stress in the fluid.  OK.  This is, this tau, the shear stress is well known.  This is something called couette flow in a small gap.  And we know that the shear stress is inversely proportional to the gap thickness and linearly  proportional to the velocity at which you move the top plate and to the viscosity of  this fluid.  OK.  You do the same force balance on this other chunk.  And then you just say that the velocity of the center of mass of snail is the average  velocity of all of the feet.  And you come out with an answer.  And it takes three lines or something.  You can do it on a napkin.  And you get the following.  So the velocity of the snail looks like this.  And there are a couple of interesting things about this calculation.  So first there's this nice pre-factor.  But the most important part is this guy over here.  So this says that the snail velocity is proportional to one over the viscosity that pad 1 sees  minus one over the viscosity that the rest of this guy sees.  OK.  Now, so what does that mean?  That means if I have a fluid with a constant viscosity, this thing cannot move.  So it just sits there and does this.  Right?  So it's basically, I mean, this is treadmilling or something.  It's jogging in place.  OK.  So it does that.  OK.  Now, however, as soon as I have any kind of non-linearity in the viscosity, so if I  have anything like if the viscosity in some way depends on the local shear stress or  the local shear rate, or I put in anything that deviates from a constant, the thing will  crawl.  OK.  So the type of non-linearity I put in determines the direction it goes.  Right?  Because there's a minus sign here.  Right?  So I can flip the sign on this by flipping these around.  So if I have something called a shear thickening fluid in which my viscosity increases as the  shear stress increases, then the wave goes in the same direction that the snail is crawling.  If I have something called a shear thinning fluid, so the viscosity decreases as the shear  stress goes up, then the wave goes in the opposite direction to the way the snail is  crawling.  In fact, if you go and look at snails, they exhibit both types of behavior.  Land snails, which have very shear thickening mucus, have waves that go in the same direction  that the snail is crawling.  And we know that land snails, mucus has this property because there is a PhD thesis by  Mark Denney that was published in Nature in 1980 on the rheological properties of snail  slime.  Mark Denney, when I talked to him, had no idea anybody would ever cite that paper, but  it's turned out to be incredibly important.  Okay, so now the last thing I'll show you is, of course, the RoboSnail climbing.  It's a snail, so it's very slow, but so this is a movie of RoboSnail climbing up a glass  plate.  So we had no snail slime in the lab, so we used whatever we had because, like you saw  on the previous slide, we could use any kind of fluid that has this nice non-Newtonian  property.  Okay?  It climbs upside down on ceilings.  It's actually easier to go on ceilings than to go up walls, right, because up walls, you're  fighting gravity both in this direction and gravity is trying to pull you off the wall,  but on ceilings, gravity is just trying to pull you up the wall, but it's not impeding  your progress, right?  So this is actually the easier thing.  And it's running now on carbapole, which is the, it's a commercial product that they  put in hair gel, so it's just a fluid that has a yield stress to it.  Okay, so, and now let me put up just the most important slide, I think, which is these are  the people who actually did the work.  So first, Daniel Tam, who did all the work on the small swimmers and is currently an  assistant professor in Delft, so he's one of the locals now.  Brian Shan, who is currently staff at MIT, so he's the guy who actually built the robot.  And Randy Hewald, I wanted to throw up there, even though I didn't talk very much about  the rheology of snail slime, he did a tremendous amount on the rheology of snail slime, which  helped us to optimize the snail as far as crawling.  And then I talked to many, many, many, many biologists who taught me a lot of biology,  particularly the most important ones, Linda Turner at Harvard and Suisd Swar is at Cornell.  And I would like to thank you for your attention.  Thank you, Begu, for this wonderful talk.  So if possible, I would like to take some questions.  It's hard to see questions.  Well, there's some question over there.  Do we have a mic or should we shout?  Well, I was wondering, when you did the simulation on the tail, it was all moving pretty in place.  Oh, yeah.  And I guess in the real world, they're not, but the results seem to be the same.  Yes, good.  That's a great question.  So the question was, in our simulations, all of the motions of the tail seem to be in plane,  whereas the real world is obviously 3D, so things can in fact move in other directions.  So absolutely, so typically speaking, and in fact, let me just go back to this one slide.  So if you look at the microtubule arrangement, let me go back to this here, you notice that  the symmetry is actually broken in this tail.  Oh, my talk is gone.  Okay, never mind.  Okay, so remember, there are two microtubules in the center, which break the symmetry of  the tail.  So the tail actually prefers to bend in a plane.  Now, having said that, there are lots of organisms that actually swim using, bending  their tail in a spiral.  There it is.  So you see here, right here, the symmetry is broken, so it tends to like to bend along  that other axis.  So most of the swimmers of the data that we looked at, they actually do bend the tail  in a plane, which is not, again, it's biology.  So there are always exceptions, and I think the ones that actually use the spiral are  very efficient swimmers.  Oh, yes?  Yeah.  Has Robosnil had any practical applications?  Oh, good question.  So the question is, has Robosnil had any practical applications?  And the answer is yes.  So that research was actually funded by Schlumberger, and Schlumberger was interested in developing  crawlers for their downhole drilling environments.  So when you drill a hole for oil recovery, you basically, you send down a slurry, and  you sort of grind up whatever's down there, and then you have to pump everything back  out, which means that you have a tube that is full of something called drilling mud.  And this drilling mud is a very non-Newtonian fluid.  It has a yield stress.  It's sticky stuff.  And the problem is that if you send a robot down and it gets stuck, you're done.  You have to drill another hole.  There's nothing you can do to get it out.  So what they wanted was they wanted a robot that would not get stuck.  And Robosnil is designed to crawl on exactly that kind of fluid.  So the stickier and gummier, the better, right?  Because it's closer to snail slime.  So after we published this, we passed that on to Schlumberger, who are now developing  those ideas into crawlers for their downhole environments.  Thank you once more for a wonderful talk.
PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_0_3503.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_3504_6059.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_6060_7259.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_7260_10463.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_10464_13823.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_13824_17255.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_17256_17735.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_17736_20531.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_20532_20807.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_20808_21215.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_21216_25583.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_25584_28787.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_28788_28991.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_28992_32723.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_32724_34487.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_34488_35063.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_35064_40559.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_40560_43883.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_43884_46055.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_46056_46559.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_46560_53195.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_53196_57923.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_57924_58031.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_58032_58079.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_58080_58787.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_58788_58847.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_58848_59687.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_59688_60611.png PhysicsFOMVeldhoven2013Anette_Peko_HosoiClosinglecture_60612_60887.png