Amy Graves:	Thank you so much. Thank you Tom, thank you Eric for this exceptionally kind introduction. Very, very wonderful. I would like to talk with you today about Of Rice and Men: The Jamming of Particles and Peoples. I wish I could claim to you that John Steinbeck said these words, "I will hug him, and pet him, and squeeze him, and name him George", but actually no, this is a meme of our culture and Tex Avery and Chuck Jones and others have appropriated it for Bugs Bunny cartoons and the like. Nevertheless, it was too appealing to miss being able to use that kind of play on words to introduce what I'm going to talk about. What does it mean for a system to be jammed? Well there are two words there that I need to define more carefully. First of all system; we are not all physicists here, so my understanding of system, I need to convey that. 
	When a statistical physicist says I'm talking about a system, we're talking about a large number of interacting entities. Sand, grain, bubbles, oil droplets in water; if you work for Exxon, they care about that a lot. Red blood cells, DNA molecules, maybe cars on a road, maybe people at a rock concert. Statistical physicists have made great contributions in the last couple of decades by venturing into fields that seem like maybe they're economics, or maybe they're sociology, and applying their methods. So we have vehicles, we have bubbles, we have corn, and all of these as an aggregate constitute systems. 
	Now what do I mean by saying a system is jammed? Well to a materials physicist, jammed would mean that the system develops a yields stress in a disordered state. Yikes. Yields stress, what's that? Well, it's like a solid in that it can withstand forces. You compress it, it pushes back, you shear it, it pulls back. That would be a system that has a yields stress, and it doesn't fall apart, and it doesn't flow like a liquid. However, it does not have the regular structure of a crystal. Here's a salt crystal: sodium chloride in a very nice, close packed, orderly configuration. Here is Gillette foamy. Gillette foamy, when you look really close, it's got these soapy bubbles of soap and water, and some kinds of oily moisturizing things that give you that smooth skin that helps to market the product. And so definitely not an orderly system. But I would argue, it's a solid. It doesn't flow like a liquid, you push it, and there's a dimple in it, and the dimple stays there. 
	Another example of this kind of rigidity allows wet sand to be walked on without collapsing and displaced and still retain it's new shape. And there are these remarkable sand paintings created with a rake by artist Andres Amadore with lots and lots of helpers. He'd create fantastical shapes in the shore in San Francisco and gradually the ocean comes and takes them over. It's really beautiful and it is due to the jammed state of wet sand. So I have one demonstration. I am a theorist, so you never know. Front row people, you're very brave to be there in the front row of the demonstration. So what I've got is wet sand and some rope. And I'm going to put the rope in the glass, and I'm going to pour the wet sand in the glass. And I'm going to pull on the rope, and it pulls right out out of the sand. Okay, makes sense, makes total sense. 
Audience:	[inaudible 00:03:45]
Amy Graves:	Oh, I'm sorry, show what? Sure. On top of it, well I don't want to get sand on the nice computer. But I'll try and do this a la carte. Or off the cart. Okay. Is that good? Alright. So that was so great, let's do that again. Now, I really do need this, but I'm going to put this rope in this glass again and then just pour wet sand on it again. Now, I'm going to say the magic words: 'a la peanut butter and jelly sandwiches'. Oh my God, it didn't work. I told you it was a theorist. alright
Audience:	(laughs)
Amy Graves:	We'll try it once more. One more time, see if it works. A little worried about banging on that. I need something really solid to bang on. Oh, shoot. It worked in rehearsal. It really did. It really did. Alright. It does work; LG has seen it work. So what was supposed to happen is that when I bang the sand very forcefully, the sand compresses and the cup is actually- levitating There we go ... So marginal. Alright. So, what we have done is turn something in flowing, liquidy state to something in the solid state, solid enough to be able to hold its own weight with the rope. My goodness. Okay. It's all downhill from here. Good. So, what does it mean for system to be jammed? I just mentioned what it means for inert matter but for entities that are not inert, mice for example, rather than rice or as Helbing would call entities like mice "particles with a will"; a will to eat cheese. It's most appropriate to think of jamming in most humane not is what happens when you squish them, but rather when they're in the state of arrested motion. 
	And so, if you have so many mice ... Or actually PETA thinks these are rats, they look like juvenile rats to me or mice ... If you have so many of them that they are jammed ... In order to understand that you really need to understand biology, physiology, psychology and cognitive science and people would argue, you also need to understand physics. Chad Snyder, the physicist says, "A crowd came be treated like a mini particle system and ideas from statistical physics could be used to model the collective effect without having to know physiological or psychological features." So let's see if that holds water.
	How about, we ask about a crowd of people. We might ask about motion so I want to spend a little time talking about motion. 1937 might be the year of the first publication like this from the Institute of Architecture of the Russian Academy of Arts, Is that a good place Father Lloyd? The Russian Academy-
Father Lloyd:	[inaudible 00:06:46]
Audience:	(laughs)
Father Lloyd:	[inaudible 00:06:55]
Amy Graves:	So these people who are cuing in Germany, you know are part of an experiment that's meant to elucidate what these Russians wrote about, the fundamental diagram. The fundamental diagram expresses how fast the people are moving as a function of the density of people, and what you can see is that the more densely people are packed the more slowly, on average, they will move. And that makes good sense. And it's true whether people are moving in a line or whether they're moving in a broad open space. Also, whether the flow is unidirectional or whether people are trying to go in opposite directions, who is walking, these are other things you might ask about and you might ask if they've modified the fundamental diagram in a detailed sense, yes, but in a broad sense, no.
	So a statistician might want to know well these is the average speed but what's the distribution of speeds like. You might want to know what is the effect of obstacles. So, I'll just show a few of these. Uni or bi-directional flow, Seyfried in 2012 showed this remarkable result that whether people were unidirectional, in blue, or whether he had streams of people trying to go in opposite directions, the flow diagram has very little change. Yeah, they are going a little bit slower and higher densities, but it's remarkable how similar these are. And why should that be the case? Well, it's an emergent behavior called lane formation. 
	So, let's see if we can get Power Point to show movement. Okay. So, here is an experiment with people going in opposite directions. And you can see that these particle people very readily create a channel for themselves spontaneously. This happens spontaneously with no leadership; it just happens. So given that we see this sort of emergent phenomenon of lane formation, it makes good sense that you might not see much difference whether people are moving in one direction or whether they're two groups of people, each trying to get to opposite points.
	Another interesting fact has to do with the correlation between the overall goodness of life in the country and the way in which people walk. No, this table that I took has to do with the free speed, people walking alone, in general how fast do they walk. This is something called the normalized z-score and Switzerland up here with the high negative numbers, is a country with a high gross domestic product and so on. And so these authors Levine and All looked at how fast people would walk. They also looked at how fast a letter would get across the country. And they also looked at whether the clocks were keeping proper time. I guess we have Eric to thank for the fact that we score high there. And clock accuracy not so much, but the rate at which a letter travels and walking speed was actually meaningfully correlated with the general, kind of, economic and social wellness of the company. So Switzerland did very, very well with walking speed, as did Ireland. And down here Indonesia, not so good and Mexico ... Definitely don't mail a letter in Mexico and the walking speed-
Audience:	So they're walking faster-
Amy Graves:	Yes. They walk faster in countries where there is better wellness by many metrics than economists ... You know. Okay, on motion of pedestrians I put these two quotes before you because I think they provide an interesting point and counterpoint. Both of them refer to the study in 2009. Here are Indian folks; here are German folks, you've seen them before ... Walking speeds of Germans and Indians. Low density's about the same. Now, you just saw a figure that showed they were slightly different but they're very different at higher densities. And the way 'The Economist', which I believe is a British publication, spins it is they say, as you probably read cause you all giggled, "This won't be new to anyone familiar with Munich and Mumbai, but Indians are just less bothered by bumping into people". So, I don't know. I find this a bit of a disturbing phrase. First of all, it's not been proven that anyone is bumping into anyone. Secondly, no one is asking whether anyone is bothered by this behavior. As a counterpoint, I really like the fact that Chatterjee, in the paper that was written, said, "Surprisingly, the unordered behavior of Indians is more effective than the ordered behavior of the Germans". So, let us realize that the Indians get where they're going faster than the Germans do and that can have quite a positive light cast upon it, not a negative one.
	As far as what age has to do with walking, here's a figure that shows not only that older people in general in Germany walk more slowly than the typical commuter of a younger age. So here, 50% of people who are over age 65 are moving a little over 60 meters a minutes. 50% of the heterogeneous population, which tends to be younger, are moving at 80 meters a minute. So, that's one lesson from this slide. Another lesson is that if you know how to ake the derivative of this integral, which is the cumulative distribution, you would say, "Oh, Gaussian". The distribution of walking speeds is like a normal curve; it's Gaussian. And it's mean is around ... Well, I have a slide ... Around 1.3 meters per second. 
	So this fundamental diagram, due to Wideman, gets quoted a lot. Wideman did scan 25 publications so I guess we would call that a meta study; meta research. 25 Publications. Sometimes people were walking in the same direction, sometimes opposing, sometimes narrow sidewalks, sometimes in open space, different places ... And derive this curve that has a per metric form. It's some equation that's got a ... It's a simple exponent. It uses an exponential. Anyway, it's a smooth curve with only a couple of parameters and it describes this fundamental diagram. How fast are you walking is a function of how dense the people are around you. And here's a little bit of data that shows how things fall on the curve from 1969. It turns out that this data set comes from a women's college. And this data set comes from a co-ed college. So we can say, "Wow, it's a little different at the women's college. They are walking more slowly and more on their sidewalks in their campus. Yet, certainly all these data do fall on the curve. 
	Now there are two points I want to highlight on this curve. One of them is this free walking speed, which is it claimed is around 1.3 meters a second with a big standard deviation around the third of meter a second. And the other leads me into the main part of my talk, which is the jamming density. So, at some density, which is claimed is sort of five and a half people per meter squared, motion stops. And I found that to be a little bit remarkable. It stops. Why does it stop? Why can't people all kind of move forward lock step? Well, people just won't move forward lock step. In fact, as Rahman says, "As pedestrian traffic density increases, the movement of faster pedestrians is likely to be impeded by slower pedestrians". So, eventually this dispersion kind of makes people shuffle and that the jamming density actually ... You would say there's really no motion altogether. 
	And this density is not the same density for all the peoples of the world. Here again, we have to admit, you know, in India the fact that the jamming density varies with minimum personal space and the less personal space you're comfortable with having, the higher the jamming density is going to be. An Indian crowd can move forward, in general, when a German crowd is all jammed together going [inaudible 00:15:17]. 
Audience:	(Laughs)
Amy Graves:	I hope I don't have to convince you that modeling of jamming is a really important social project. It not only helps day-to-day problems of people moving around in public spaces but it also impact extraordinary problems, as when there is an emergency, there needs to be an evacuation, there's a crowd. Understanding motion near repulsive and attractive objects is important, so this slide is meant to address that issue of the many difficulties, for example, during the Islamic Hajj, the traditional pilgrimage. Particularly dangerous is access during the 'Stoning of the Devil' ritual. So there are these monuments, the jamaraat. I'm sorry; I don't speak their- But the jamaraat monuments ... They're three monuments. They represent demonic presences and the idea then one must approach them in a particular order, stone them in a particular way, and then step back and let others come through. And that's particularly difficult because there's kind of this circle around the monuments. So there's a radial flow of people inward and then they need to come out again. There's also this transverse flow of people. There have been a lot of injuries and groups of scientists, in particular Al-Ghadi Badal have been very successful at writing a set of equations that model this behavior and it's actually called the jamarat model of pedestrian flow in this situation. Here you see pilgrims on the way to the jamaraat.
	Another situation that's really serious is understanding motion of large people near doorways and passageways. I took this from the web. It's a recent shot of Liverpool fans who are, in a way, celebrating the fact that the British Prime Minister finally acknowledged, decades after a terrible tragedy in which 96 people were killed at a Liverpool soccer game, that it wasn't polygamism, that it wasn't alcoholism, that no one was leaving in an inappropriate way so that 96 people were crushed to death, but rather it was crowd dynamics and it was physics. And it was a little bit of blame put on the police because the police didn't act quickly enough to evacuate people who were hurt seriously but could have been saved if they'd received prompt medical attention. What happened was a gate that had normally been closed, or it had been closed in two previous seasons, was left open and it led to a narrow passageway and that passageway lead to a holding area with a lot of fans that was already full and no one knew what was ahead and many of the fans were crushed against the concrete barrier and tried to escape by climbing onto the field; horrible situation.
	And in response to situations like that there've been some wonderful projects. The German Federal Ministry of Education has funded the Hermes Project, which is this fabulous tour de force where applied mathematicians, computer scientists got together and created a system with cameras, with image recognition, with software that will project about 15 minutes into the future for a venue and will say given that all these people are where they are right now, in 15 minutes I would expect them to be here and can alert the staff to, "Okay, we need to make these modifications, door escapes, this and that. So. The Hermes project sounds like a wonderful innovation. There's also a private company called ... It has a pedestrian dynamic simulation ... In Touch ... In Control; it's the In Control company. So, if you're the manager of a large venue you can actually buy commercial software that's gonna map out your venue, that's gonna map out your seating, that's going to take a count of who is going where, when, and do the same kind of predictive magic for you to be able to help you ensure the safety of people who are at your venue. 
	So, that's stuff about people and jamming. Now I'd like to switch gears and talk about physical applications. So if you're not an animal in a crowding situation, jamming is actually quite a cool subject. Jamming is phase transition and so here what we've got is a phase diagram. For those who you who don't do a lot of thermal physics, what a phase diagram consists of is some axis's that represent control parameters, like how dense is the system, what temperature is the system. Here, are you stressing it from the outside or not. And the inside here, when the temperature is low, when the stress is low, when the density's quite high, this is one over density. Now here, we have a jammed phase. And then let's just say we move along the density axis at a certain critical density. So out here one over density's getting large, the density's getting small. 
	This is a very special point that Lew and Magel have proven. It's a point of phase transition like water to steam, water to ice and it's and it's called Point J. So this is exciting to people who care about statistical physics. It's also kind of exciting to people who watch Indiana Jones movies. LG and I were just watching Indiana Jones and the Crystal Skull the other night and Indy and Marian, they're like sinking in this thing. It wasn't quicksand, it's something. I don't know. It's quicksand. So they were sinking in this stuff and he said, "Don't struggle. You'll sink faster". Well, what do you do if you struggle? If you struggle, you stress it. You stress the material around you. If you stress the material around you and the material happens to be jammed and you come out of your ... Oops ... Unjammed liquid, down you go. So it made total sense.
Audience:	(laughs)
Amy Graves:	As much as an Indiana Jones movie can make sense. So jamming is cool. Here's a little cartoon from the Seimans and Van Peck introduction. And you can see these featureless blobs. They are the members of our system. At low density they're unjammed and at a critical density they jam up. And then at a higher density, they're still jammed. You can ask about interesting things like the pressure. Here there is no pressure provided by these guys. Then, at the critical density ... This is the excursion from the critical density. Below zero, we're below it, Above zero, we're above it. Really a five means volume fraction. It's actually not just the density being technically correct. This is the volume of the white space that is taken up by red guys. So, at the critical volume fraction, pressure starts to rise. In fact, it rises linearly and that's something folks are so excited about; that it's a universal thing that the pressure rises linearly, independent of many other features of the model.
	Another important thing ... I don't know if you would think of this first hand as being important. I adore it. It's just the contact number, it's a number of neighbors. So immediately below the jamming threshold, why should any particle be touching another particle? At zero temperature, It just isn't. It's just phenomenally unlikely. Suddenly at jamming, the contact number rises to a certain value. It's jammed up. Everybody needs enough neighbors to be stuck in their place, to be stagnant. And not only is that a point of staticness, it's also a point of isostaticness. So James Clark Maxwell, who most of us think of as one of the founders of electromagnetism, actually was the first person to talk about isostaticity. Just so you know, if the number of degrees of freedom, that is the ways that any particle can move, is exactly equal to the number of physical constraints, the things holding that particle in place, it is perfectly rigid. And isostatic means not too many constraints and not too few constraints. Here's my little illustrative slide or quiz, okay, where one of these shapes is isostatic and one is not. If you built it out of wood and you out nails there, which one of these is isostatic? Which one is it? What do you think? Talk among yourselves.
Audience:	(laughs)
Amy Graves:	Talk to the person next to you, decide. This is what we do in physics three. Oh what do you think, I don't know. They both look pretty solid. Okay, time. People that think it's A signify by saying I, or A.
Audience:	A.
Amy Graves:	Great. The people who think it's B.
Audience:	I.
Amy Graves:	Oh, thanks. Okay, actually truly it is A because truly B can be nudged and turned into a parallelogram and it's not stable and you have to nail a cross brace onto it and there you go. And then you got two triangles and it's isostatic. Okay. I don't build many things. Took me a while to get okay with this, but I'm okay with this now.
	Alright, so I had to work rice in somewhere 'cause I call this a rice man. So here comes the rice. But not man. Let's talk about gumballs. You wouldn't believe how hard it is to find a naturally occurring grain and it's spherical. Quinoa, not really. See, I don't know a grain that's spherical. I put in-
Audience:	Cous-cous
Amy Graves:	Cous-cous. I looked at cous-cous. It's a little pudgy.
Audience:	[inaudible 00:24:37]
Amy Graves:	Yeah, when it's cooked it's spherical. When it's dry, you're right Laurie. Before you cook it, it's got a little bit of an anti-[inaudible 00:24:43] to it. Yeah. So isostaticity is actually the exception, not the rule. If you have a very stumpy grain of rice, well you paradox because if it were exactly spherical James Clark Maxwell would tell me I need six contacts to have isostaticity. But if it's elongated, it's like this. It can wiggle. It's not just x-axis, y-axis, z-axis, it's also, "Oh, I can wiggle like this". So you actually need more constraints to keep this thing from wiggling. Well, alight you actually, if this thing were like rice it would need 10. So what if you have really stumpy thing that's only slightly ... And the answer is in your data. A spherical particle at jamming has six contacts. As soon as it gets to be slightly elongated, it zooms up to have the right number 10 to be isostatic. But in the middle, it's not isostatic, it's hypostatic. You can jam systems of spheroids that still have freedom, but they're still jammed. They still have a bulk module [inaudible 00:25:46] So there is my nod to the rice.
	What I'd like to do to motivate the fact that you've been studying jamming with the idea that we're trying to enhance jamming. I'd like to tell you that sometimes jamming is desirable. Not with human beings in a public space, but for example, with these things called soft jamming robots. So rather than an articulated robotic hand or an articulated robotic claw, we think of something that's for all the world like a balloon that's filled with coffee grounds. In fact the first prototype did have coffee grounds in it; smelled really good. What you do is you have a system here I'm not sure is we should call it hydraulics. It's not a fluid; it's air. And air is sucked out of the balloon and the balloon becomes hard and jammed. And anyone who has ever bought coffee, it's vacuumed packed, those who buy these bricks of coffee in the super market. And then if open it up and out a spoon in it, it's all flowy. It's not hard. Well, you've just seen a jamming to unjamming transition. So, suck the air out of it, it becomes rigid and hard and then poof the air back into it, it becomes soft and it's amazing at picking stuff up. And in the still picture I have here, it's also amazing at playing darts. It's the thing you want to take to the pub. 
	So let's see if we can get the movie to play. It's seems to take me two clicks to make movies play around here. So this is a Cornell Chicago collaboration. I'm gonna have all the movies playing at once 'cause it's a little dull to just have one so ... Let's see them all. Oh, the middle one gonna show you [crosstalk 00:27:22]Little things, big things. And this one is- oh yack, yack yack, turn down the sound the sound. I'm gonna move this one forward, show you the robot kind oozing around. He we have the robot shooting baskets. Here we have the robot gripper. Oh there it's moving about. So how is it moving? It's because different chambers are inflated with air at different moments and synchrony to actually make it locomote. That's very, very, very clever. It also happens it could collapse, ooze through a little crack and then puff up again. It's pretty terrific. And so in this one we've got that brick for just being rally good at picking up. It can pick up an egg that's uncooked, it can pick up a pen, a dime. Much improved from anything made of mechanical metal and here it's just having fun, kinda shooting springs and bolts into the different boxes. 
Audience:	(laughs)
Amy Graves:	So-
Audience:	[inaudible 00:28:19]
Amy Graves:	Isn't that cool? Love those jamming robots. So maybe in a few years we'll have the sophomore jamming robotic team. I don't know; the robotics team is pretty awesome already. 
	Let me say a little bit about simulation. How should we simulate ... Well what do we care about? Do we care about statics or dynamics? What do I mean by that? I mean static properties might be well, at what density does the system jam up? What are the fores like? Here is a very popular exhibit at a science museum. It's got these little piece of the plastic discs lit in just such a way that when a child comes up and moves a piece of metal to stress the system in a particular way, the lines have large force. The stress lines show up as a bright spider work web of lines. And in fact here and like this, a nice simulation by Raaj Diangrue in 2008 where they simulated disks and got these spidery lines. Oh, looks similar, in fact statistically the distribution of forces, is uncannily similar from the simulation to the real world application. So, you might be concerned with how the force lines are distributed in the system. How many near neighbors-that speaks to isostaticity as a really fundamentary system of just the right number or near neighbors. Or was it very packed in? Overly constrained? And the role of obstacles or attractions. 
	So this is the one that I want to show you just a couple of results about. I'm sensitive to the fact this is not a technical audience, so I will try to warn you that something technical is coming and let you know that now is a good time to check your cell phone for messages. One project that we've had some success has been the simulation of jamming around fixed particles. We're in a collaboration with Professor Andrea Lui at Penn and her remarkable grad student Carl Goodrich has been really the big mover and shaker on this project at Penn. We've had several Swarthmore students on the project: Sam, Almondine, Elliott, who's now at Cornell and Sammmer ... Are you here Sammer? Hi Sammer. Sammer is hard at work at this stuff right now. He knows more about it than I 'cause he checked the cluster at Penn this morning, maybe. So he knows more about our data than I do at this moment. So we're very lucky to have Sammer and lucky to have had these other students as well. 
	Okay. Jamming around fixed particles. What am I talking about? Well a lot is known about what happens when you take an empty system and you fill it with particles and then, you know, jams up at a certain density. Surprisingly, not much is known about what happens if you first have that system filled with these landmarks. Maybe it's a two dimensional system and you've etched pillar in. Maybe it's a three dimensional system and you've got some kind of webbing in there and then you're introducing the moieties that are about to jam. These are the kind of two dimensional lattices we've been playing with. These are actually over sized. Our ideal is to have just points that are infinitely strong but infinitesimal in size to hold the jamming system there. So we've got them in a hexagonal lattice, a square lattice thrown at random. And this is something, quenched disorder. I would not have thought of it but it turns out this is really important in the superconductivity community. It has to do with pinning of vortices. It's also interesting in the glass community. So we did these as well. And what I mean by this picture is these are disks of the type that I'm going to put in and let find their place, but we throw a bunch of them in it first and glue them down and they have no mobility.
	Physicists tend to love simple models. There is this joke about a cow ... A problem having to do with cow needing to get it's water from a feeder ... It's actually true, I hear. It needed to drink some water and every time it came up to the water feed, because it was metal, actually got a shock. And so they brought in a physicist to try and figure out how the cow would not be shocked and he came back in that era, all physicist were heed with the report and the first was "Assume a spherical cow".
Audience:	(Laughs)
Amy Graves:	So, we physicists love to assume spherical cows. There they are in the field. Not grazing, but in the field. So, here are our spherical cows. There's disks in 2D, there's spheres in 3D, they kinda overlap. They're soft but when they overlap it costs energy. Another way to think about it is exerts forces on each other. And the more overlap, the more force. Hey want to stay apart. We've simulated zero temperature. We're not gonna share the system in what I'm gonna show you today. There's not gonna be any friction. And here's our protocol for the CS folks in the audience, if you care the codes happen to be in this language, C++. So we first position our fixed particles then we throw in our mobile particles N of them, random positions then we equilibrate the system to find the lowest energy configuration. 
	So this would correspond to us working at zero temperature. The algorithm if any one cares about ... One algorithm is called the fire algorithm and we also use a modified Newton's method. It seems to work; we seem to find an energy minimum. Do we find the energy minimum? That's too hard a question to answer. And then we remove the rattlers so let me go back and forth between two slides and see if you see any difference. Look right here. Wait. So .... Boom, boom. Boom, boom. Are folks seeing that? Okay. Cool. About 3% of the particles a not going to have any neighbors. If you shook the system, they would go rattle, rattle, rattle, If you turned it upside down after gluing the others they'd fall out. So we do remove the rattlers. They're not part of the mechanical stability in this system. Here's one result. I'll throw three results at you. One result answers the question how does the jamming threshold change with the number of fixed particles? And the answer seems to be this is a square lattice of these point like particles, the threshold drops linearly, with the fraction of pegs and that's really good. We've gotten a reduction of the jamming threshold by putting in zero volume fraction of things in here. 
	Now, an interesting thing happens. In the jammed system, either nothing is stuck or everything is stuck if there are no pegs there. But if you have ... I'll skip two slides forward. Once you put in these obstacles you have the situation where yellow is rattlers; a lot of rattlers. Some particles here, the light green ones that are stuck. The dark green ones are actually fixed particles but they don't stay in the system. 
	So you have this extensional question: Shall I call this jammed or shall I not call it jammed. And it really has no fundamental answer but I think the practical answer is this isn't a jammed system. This is what we want to talk about when we say, "Oh, it's a solid. I can squish it and I'll push back at me". This won't if you squish it this way. So we want to throw out finite clusters and only keep the infinite clusters. Here's a system that's jammed and how do we know? Well, Elliott Padgett 13 wrote a wonderful algorithm that traces along all of the particles that are not rattlers and says, "Have I actually got a spanning cluster?" If people who know the lingo ... Percolation. It was a percolation algorithm. So he saw that things percolate and this allowed us to go to much larger numbers pinned. In fact, infinite numbers pinned, you know, because now we don't have this ambiguity. So really happy that we have that capability in the code now.
	Here's our second result. What lattice in geometry supports the jam structure most readily? Interestingly, we actually got an answer; that there was one in two dimensions. A hex fixed lattice with exactly the same density of particles supports the jam structure measurably better than a square lattice does and measurably better than the random lattice. And this is this really interesting question that speaks to "How do I build something and make it jam more easily, with less stuff in it or quickly?" And clearly three dimensional calculations are important to do and we have a routine that those three dimensions ... We have certain things that Sammer could tell you about before we get this going on this project, but certainly by next summer we'll be able to answer this question for three dimensional lattices as well. And there's more choice. I've been told by a wonderful applied mathematician that whatever question you ask in two dimension the answer the hex lattice. But in three dimension, there are lots of wonderful lattices that answer different similar sounding questions about graph theory. It'll actually shed light on the fundamental mathematical nature of the jam system if we can answer this question in 3D. So we're really happy that we're going to be able to do that.
	The last result, I don't think I'm gonna show you really, really what it is in the interest of time, but I'll talk around it. Since jamming is a phase transition, what generic features of phase transitions, in particular critical exponents, do fixed particles allow us to calculate? So if you've had a statistical physics course or if you've taught one you know what I mean by critical exponents, if not, again, this is a good time to check for your messages on your cell phone. I'll just talk around it just a little bit. We're writing a pre print called 'Pinning Susceptibility: The Effect of Dilute French Disorder on Jamming' and I'll flip real quickly through the couple of slides that mention it. 
	Dilute, that means we only have a couple of obstacles. Boring, you know. What can two possibly do to a huge system? Some of the systems Sammer has run have 4,000 blue particles in them. And two fixed particles? Well, remarkably the point of phase transition is a very delicate point for even putting in two fixed particles can get it's message across the system. And so it actually has some sense and those statistical physics majors in the audience maybe will feel okay if I say there's an analogy, something like the Issac model, there's a lattice of spins, there's magnetization and when you differentiate it you get this heap called the susceptibility. It's how susceptible the system is to say, "Okay, I'll magnetize this way. Okay, I'll magnetize the other way".
	In an external field, Bob Griffiths and then Peter Reynolds and then Lincoln Chase and Andrea Lui got this cool idea that you could use this ghost's spins to get it's susceptibility. So what we have is these pins acting kind of like ghosts; kinda like our little decoys in the system, and if you look at the probability of jamming and then you take the derivative with respect to the density of pins, damn if you don't actually get a peak, a peak which corresponds to a susceptibility, if you will, so we call it the pinning susceptibility. The codes that are running now that Sammer is shepherding through the queue are hard at work finding this critical exponent. So in the limit of an infinite system this should go to infinity and this number says how fast it goes to infinity. Right now we're getting ... Did I get it right Sammer? 1.2? Cool. Okay, so we're getting 1.2 in two dimensions. We're getting it for two different kinds of potentials so it doesn't seem to care what kind of interaction the spheres have. The big question, does it care whether it's two or three D. And for people who know about this I'll just say three words: upper critical dimension. So, that's enough of that.
	In the last, uh wow, 15 minutes, I'll try and take less, that are allotted to me, I want to switched topics and talk about dynamics rather than statics and say suppose we want to simulate people or particles and we care about their dynamics. Are they jammed at a certain density or rate of entry? And really when you wanna talk about people they get stuck 'cause no one can get out that door. It's more appropriate to say, "Are they pinned?" Or "Is it a situation of clogging rather than jamming?" People argue about this. What's there flow rate? What emergent behaviors exist? Do you remember those lanes that you saw in the video? Is there herding behavior, external forces, role of obstacles or attractions? All of these are features that you might wanna know about if you're thinking about the dynamics. So pedestrians are particles. Which ones are you gonna simulate? I don't want to paint with too broad a brush. I'll say that these two different realms have a lot in common though they have very fruitful differences and you have to be sensitive to it. 
	Pedestrians, or little plastic spheres, you care about the flux of these as the function of the corridor width or both systems. You care about the density and the geometry and how they affect the flux. You see similar arching going on. So when there is a jam, here ends to be a little structural arch there that our engineering colleagues would recognize as something that supports itself. And unfortunately, it supports itself and it keeps everybody else from coming through the doorway. Yet, you have to admit that with people there is a motivation, which isn't just "Um, gravity's pulling on me". There's a more complicated motivation. There might be stimuli that have a psychological component and they result in a behavioral reaction that might be quite personal. And also, I don't think there's an analog; at least not in the granular material field to injury. We don't even care about injury. These are tough little things. We care, maybe, about global fracture and flowing but we don't really care about each little thing being harmed. Yet, there is a claim that here are two kinds of situations. And one kind is a simple, or standard, situation like people are leaving a lecture hall that they leave all the time in a building that they know very well. And in a standard situation, reactions are automatic and characterizable and you can use what's called the social force model. 
	So Helbing and Molnar take this point of view; others take this point of view. If you want to simulate, you could do it based on forces whether it's people or whether it's little granular things. Or you could do a rules based simulation and people in the artificial intelligence community are more at home with those kinds of simulations, rules based, agent based simulations. I'd like to show you an example from outside and an example from inside Swarthmore. Here's a classic rules based simulation of a system. These are android birds, they are called boids. Craig Reynolds came up with them in 1986. And as these boids fly around, what I hope you'll keep in mind is that there are only three rules dictating what they're doing and every boid has the same three rules in mind. One is cohesion. No boid wants to get too far from the center of mass of the other boids. The other is repulsion. You don't want to hurt your wings; you want to bump into another boid. And the another one is alignment. You want to go the general direction that the flock is going. So every boid is looking or sensing and somehow the boids around they pick the average velocity vector and they say "I want to go in that direction." 
	So whether it's a really simple project that the student did for a programming course in MAT lab or whether it's a really amazingly rendered flock of boids or whether you're watching the movie 'The Mummy' and see all these little insects scuttling around or whether you kid or you are playing on the Play Station and see lots of beings doing things ... Typically if you see lots of beings doing something, no animator worked to make each of them make a lot of autonomous decisions. Every one of them is following the same set of rules and it's a tiny set of rules. In this case, an economical case, only three rules give extremely complicated motions. 
	So that's pretty beautiful and here I have an example of something that's a little more paired down. It's our easy java simulation of people exiting a room. The student who worked on this was Mariam Bondehasen. Mariam did this when she was just a rising sophomore. She just graduated last fall. So I'll set this going and what you'll see is that we're going to set the density of people in this room to 40% and we're going to let them try and get out this door. And they'll try to get out this door. Six people, seven, eight, nine have exited. That's the green line. A few people are hurt so the blue squares turn black when people get hurt. It's all fun and games til someone gets hurt. She's increasing the density now, or I am actually and a lot more people are getting hurt. And you can see ceratin realistic features as the waves of hurt actually travel backward like there would be a compressional wave that will travel backward through the crowd of people. This is the motivational part. People want to go through the door so these arrows show which way people want to go if they're occupying a certain square and they want to go with more enthusiasm the more arrows are blue and less that they're red. That's our rules based simulation.
	There are also force based simulations. So let me just give you a feeling for why they're different, how they're different. The particles feel forces. They feel forces from the other particles and they feel forces from the environmental features. And then they do force equals mass times acceleration. They move in response to the forces. However, if you're not talking about inert matter like grains of sand, if you're talking about animals you include forces like desire and the social forces.
	So just additional forces to put into your calculation. Here's a nice schematic that I took from someone named Maron who is in a computer vision lab in Florida that this particle person would really like to move toward this goal however this person's actual velocity is pointing this way because this person is feeling certain interaction forces from other people. This person, that avoidance rule doesn't really want to walk into this person. 
	What's mind blowing to a physicist is that we call these forces okay, they are repulsive and attractive fine. Their time and velocity dependent. Physicists don't usually deal with forces that are time dependent but if I see a store window and I'm really attracted to what's in there, and I want to go look at it, I'm not going to look at it forever, I'm going to eventually be like enough. You know, and I'm going to walk away.
	So there is a time dependence to the forces, and also they don't obey Newton's Third Law. Just because I am walking towards someone and move back, I don't want to bump into them, they don't even see me, they don't have eyes in the back of their head. So there is no conservation of momentum, there is no Newton's Third Law thing going on with these[inaudible 00:47:45]. Here, two simulations to show you, it's the last thing I want to show you before I sum up.
	Force space simulations, we wrote them in this environment, easy Java simulation by Paco Escabar, and Wolfgang Christian, and his students Vie and Travis who did an amazing job on these. I really like this one, it doesn't produce any result. There might be one novel thing about it. We have two teams. The blue team would really like to get to a goal up here at the top and the red team would really like to get to a goal here at the bottom, so here they go. Go. Yay.
Audience:	(Laughs)
Amy Graves:	[inaudible 00:48:30] And what you see is, you really shouldn't call it lane formation but what there is, one team will break through the line of the other, and then the other will break through the first, and people call that oscillations of bottlenecks. So there will be a oscillatory behavior back and forth.
	Okay so here we see, yeah there's the oscillation, first blue then red, and this is just a bunch of different trials where we just run it repeatedly. The last, okay bonk, alright everybody got where they are going. The last trial I put in here because everybody doesn't get where they are going. And that's something kind of new. 
	Go. Okay. So I don't know. Gotta give it a name, and get some grant money for it. Oh no, hey little help. I would call that dynamical trapping. And that's something I've never read about but for a certain velocity of particles for certain types of interactions, you would actually get some particles trapped forever on the wrong side. 
	So that's an answer searching for a question. And maybe that's something that we can explore in the future. And the last simulation I want to show you is a really multi-purpose one. We can watch the numbers of particles exit it, and monitor their energy. We can put on gravity, which means they are [inaudible 00:49:57] particles or we can have them be people, we can have them be pedestrians, mono- disperses. Are they the same size? Blockade, you'll see inside the exit, is can they see where they are going or is it smoke filled and when I turn on side the exit, the ones that can't see the exit don't know where to go, and actually on this version of the simulator they don't wander at random, they just kind of respond to inertial forces. 
	So let's just let this go. I just want folks to see the different features that you can build into one simulation. Off they go under gravity, we're losing a lot, so we replace the ones we lost in at the top. The color corresponds to the velocity of the particles. Okay now they are pedestrians. You don't really see too much difference. But side exit, now these guys are lost. They're heading all in the wrong direction cause they just suffered an impulsive collision. And the ones near the exit know what to do, they're trying to go for the exit. And so one can monitor how many folks get out as a function of the different situations. 
	What am I doing here? Oh I'm going to make two doors. So the questions is, is two doors better than one? Let's say they both have the same width. No, because you can get transient arching, well if they are too narrow you can get arching. But an outstanding questions that hasn't been answered generally is under what situations is it better to take one wide door and make it two separate doors. And the answer clearly depends on kind of the rules and the system you're simulating. This is a blockade and we can move it around. And we almost had a great idea here. We did. But we got scooped in 2011 by another group.
	So I think I'll just stop the simulation there and show you the next slide which is that, you can actually enhance flow with a strategically placed blockade with a strategic geometry. So here we have no blockade and then we have one that's sufficiently small that stuff can flow to either side. And you turn kind of chaotic flow where the particles are bumping off each other and getting in each others way, to more smooth layer like [inaudible 00:52:13] flow. So the flow rate actually increases.
	Then if you make, this is called the waiting room affect, I guess everyone is all blocked up here to see the doctor, and then underneath here there's a big vacuum. And here the obstacle has gotten so big that we've got bridging and blocking that comes from the obstacle itself. So it's kind of delicate to find the right size obstacle to make that happen. We have seen it. 
	So in conclusion, I hope some of the things you'll take away from this talk, I hope you'll take some of the things away from this talk. This is too long a list. Jamming applies both to animals and to inert things. Jamming can be frustrating or even lethal, or it can be beneficial. It is understandable from the point of view of statistical physics. We can simulate jamming via rule spaced, or force spaced methods. We can look at the static properties, we can inquire about the dynamical properties. And as[inaudible 00:53:04] in collaboration with Penn, we've done C++ simulations with fixed obstacles to show how point J moves when you change the density. What obstacle geometries actually help jamming. Are there new critical exponents? Yes, there are, associated with the jamming transition. There's lots of work we can do in the near future. We need to vary the obstacle densities, and assume that when the obstacles are really packed in, we're going to see some really new kinds of configurations. It's going to be qualitatively a different picture of what it means to be jammed when the obstacles are quite thickly placed in the system. 
	3D systems are important looking at mechanical properties are important. And finally that we've done EJS easy job assimulations. They're good, they can switch between dynamics of particles and people. They're really easy to use and modify. One can give them to a student who hasn't had a computer science course yet, and they can be doing authentic science in a very brief time. But things have gotten so sophisticated in the computer science community with such beautiful simulations that are optimized with mind blowing graphics, that you know pedestrian safety codes are very high level out there in the big world. 
	And so our simple codes are still awaiting a novel problem that we can solve and write about. So I would like to thank everybody, my colleagues at Penn, the Lou and [inaudible 00:54:29] groups. The [inaudible 00:54:31] students who've worked on this project. I have the most supportive department, just the most collegial people. I thank the department of physics and astronomy for being the wonderful people you are. I thank my supportive family.[inaudible 00:54:44] And the people who provided the money, [inaudible 00:54:47] research fund, the National Science Foundation, the Division of Natural Sciences, Gene Lang who gave a grant for a sabbatical. And thank you for listening.