 Okay, let's go ahead and get started. So welcome to the first scientific talk for the hands-on school. Before I introduce the speaker, I'm going to make one announcement. I'm going to ask the question. So we had the whole ordeal with the bank this morning. How many people did not make it through the bank? Raise your hand. Okay. Okay. Would you come see me after the talk, but before we go to the hands-on session, we'll make a plan for a plan B so you can get your money tomorrow. Okay. So come see me. Okay. So I'll just let you know the procedure for today is we'll have a talk and then immediately afterwards we'll get together. We'll have before you leave from here, Professor Shaddick will pass out a schedule which will give you the schedule of the hands-on sessions that you'll attend. So you'll learn which is your first session today along with the rest of the sessions. Okay. So that will happen immediately afterward. And then after that, we will progress up to the various locations. Most locations will be up at the M lab, the multidisciplinary lab. So I'm going to ask the hands-on session leaders to stick around and basically help guide the group as a whole up to that session. The only difference or the only session that will remain here is Professor Chembo's session. So if you, and that will be in the UN room. So you'll learn what that is shortly. If you're in Dr. Chembo's session, when you get the handout, you stay here. Stay with him. Everyone else will progress up to the multidisciplinary lab, the M lab. Okay. Any questions or any other issues? Oh yes, I'm sorry about that. That's right. There's also those sessions. So stay in your seats, we'll pass out the schedule and then we'll tell you which groups go where some, it's more than one session stays here. And those that will go to the M lab will congregate as a group and head up to that lab together. Okay. So it's my great pleasure to introduce Professor Harry Swinney from the University of Texas. He's one of the founding directors of the hands-on schools. And he's going to tell us about the philosophy behind tabletop experiments. So I turn the floor over to him. So I'll be talking about particular type of hands-on experiments, experiments in which we observe the emergence of patterns as some parameters vary. You read a lot about science and hear a lot about science in the news these days and that's great. Science is getting a lot of publicity. And often the science that you hear about most often is big science. Where you have projects that cost $10 billion or even $20 billion involve thousands of sciences in a single project and they take periods of decades. The large Hadron Collider was conceived in the 1990s and constructed in the early part of the 2000s, came into operation in 2007 and in 2012 made this major discovery, something that had been anticipated for a half century, the discovery of the Higgs boson that was expected based on the standard model of particle physics. And this experiment is continuing and we, our university in Texas have a number of members of this collaboration but as I said there are thousands, there are two of my colleagues work on the Atlas Detector which was one of the detectors that saw the Higgs boson, detected the Higgs boson. Another large project which is much in the news recently is one that was conceived in the 1960s to look for radiation, gravitational radiation that goes back in concept to Einstein's equations which have a form of wave equations, these waves that were exhibited by masses and large masses interacting, in this case the waves that were detected were produced by two black holes that collided and gave ripples in space and time. So this was a major discovery, very exciting after at least a half century of anticipation and experiments, first systematic experiment was 1967 or so. But it failed until this recent experiment to detect gravity waves. Another large project which is costing, will cost of order of 20 billion dollars is the project it's under construction in France, ETER to produce a plasma that will be very hot and you'll have deuterons and tritium atoms colliding and fusing together and releasing energy and there will be more energy released than taken to heat up this plasma to very high temperatures, very high temperatures are required because you have the economic repulsion of these protons that must be overcome to get them to fuse, it must come down within a distance of 10 to the minus 15 meters so it must be very hot. So these are the kinds of science projects that are most often in the news but they're not what we're here to study this week and not what I'm here to talk about this week. There is science that can be done on a smaller scale, smaller scale than 10 to the 9th dollars let's say a million times smaller, maybe a thousand dollars, maybe less over time of a year or so, a couple of years, scientists and maybe two students can use inexpensive equipment such as webcams that we'll be using this week, interface between the computer and the experiment to control the experiments and Arduino or Fidget controller and we have enormous computational power available that was not available even 25 years ago, the laptops you can buy for $500 are as powerful as the largest supercomputer of 1990 and the storage that's available is enormous and one day in the experiments that we do on ocean physics, dynamics of oceans now in my lab we generate a couple terabytes of data inconceivable even a few decades ago and we can do computations, we can solve the equations of motion, the partial differential equations using MATLAB we can build models and do a lot of science at a fairly small investment, a lot of thinking power but not a lot of dollars so let's look at some examples the problems I'm particularly interested in discussing today are those in which we take a system in thermodynamic equilibrium and drive it away from the equilibrium state, we impose a gradient and increase the size of the gradient, we move further away from the thermodynamic equilibrium state gradient could be gradient temperature or velocity or concentration or some other variable, this type of problem was studied a century ago for systematic studies consider a fluid in a box at a uniform temperature say a gas or a liquid in a box if you look at the motion of a molecule and its neighbors the motion of one molecule affects neighbors that are only a few molecular diameters away, a few nanometers away now if we heat the bottom and hold the top plate fixed at a lower temperature you can imagine what would happen and you all know from, everyone knows from putting a pan of water in a stove you heat it from below and after you've applied heat for a few minutes you see the bubbling of the fluid, you see the motion of the fluid, the fluid is no longer in the stationary state you have convection so it was a problem of interest a century ago and the question was is there a well defined temperature difference between the top and bottom at which this motion begins at which you move away from the stationary state and have a new kind of state so this problem was studied in the laboratory by a Frenchman named Henri Benard and those experiments inspired Lord Rayleigh to investigate the problem theoretically and he found that there was indeed in his simple model a critical temperature difference beyond which you have the onset of convection so fluid rises, the warm fluid rises here and goes down here so you have a convection role and these roles become more intense as you increase the temperature difference delta T. Now he did an analysis and predicted the temperature at which temperature difference at which this would occur and it didn't result from the theory did not agree with the experiments of Henri Benard, they were off quite a bit and no one understood why so the leading scientist and a number of leading scientists at the time said well maybe we should select a simple problem what could be simpler than two infinite parallel plates one moving with respect to the other so if they are stationary there is no motion of the fluid if you move the upper plate then the fluid near the upper plate is moving at the same speed same speed as the fluid there right there and there is linear variation of velocity with position between the plates as you can calculate quickly from the fluid equations, Navier-Stokes equation but how large does this speed have to be for the fluid to have a flow that is different from this linear variation with position can that be predicted so a number of leading scientists at the time tried to calculate this critical velocity at which the fluid would develop a pattern and they failed but another geometry was considered by a scientist at Cambridge University G.I. Taylor he was an experimentalist and he was interested in doing experiments to compare with theory but he said you know it's very difficult in the laboratory to have two infinite plates they tend to be finite in size so he took the two plates and made a drum made a circle so he has two concentric cylinders and the fluid is contained between the two cylinders and each of the cylinders could rotate in this experiment but let's say suppose just the inner cylinder rotates can you predict as you begin from zero rotation rate and increase it can you predict the critical rotation frequency at which a pattern would form and this is often expressed in terms of the dimensionless number the Reynolds number but omega is the rotation rate of the inner cylinder and he calculated that at a critical rotation rate vortices fluid vortices would form between the two cylinders and they would be in the shape of a donut and these donuts are stacked in the axial direction and let's see yeah he obtained this theoretical curve and he also did experiments so he did theory and experiments and on this graph you have the speed of the inner cylinder here increasing vertically and the speed of the outer cylinder in the horizontal direction here horizontal axis so this point is thermodynamic equilibrium both cylinders are at rest and as you increase the speed say of the inner cylinder with the outer cylinder at rest you're going up this axis at a certain point he predicted that the pattern would form actually knew of the form because he did the experiment first and then he set about to predict the point of instability so you see the experimental points here in red and the theoretical points here in these green dots and agreements remarkably good within a percent or two for the between the experiment in theory and this is a quote from his paper said previous attempts by some pretty good theoretical physicists Kelvin Lord Rayleigh Hopf we all know summer felt to calculate the point at which a fluid would become unstable and pattern would form have failed calculate the speed at which but here's the example where this was done now this is a pattern this is actually a picture taking him in our laboratory but it's similar to the picture that G.I. Taylor obtained in his experiments by injecting dye into the fluid the dye collects at the boundaries between the border seas so if one of these black lines you have fluid flowing out the next one you have the fluid flowing in but the dominant flow is in the as muthal direction super post in that you have this toroidal flow as you saw yesterday as I mentioned you can increase the speed of the inner cylinder further and you get further well-defined transitions that occur at a particular rotation frequency of the cylinder you have this time independent flow the velocity field fluid particles are moving but the velocity field is not changing in time at any one point in the flow but in this case you have these border seas develop waves above a certain critical speed of rotation of the inner cylinder and if you go higher ultimately you get to a flow which is not periodic it is something more complex called chaotic flow and if you go to very high rotation rates you have turbulent flow in a turbulent flow you have a wide range of spatial scales and temporal scales which are involved in the description of the motion now this is where the inner cylinder only rotating what if you rotate the outer cylinder as well as the inner cylinder to make a graph like this but look above this line here and see what happens up here well that was done in an experiment which I will mention in a moment but this is how we in the lab session here that we have up on the hill will characterize these different flows will take movies digital movies with web cam and look at the intensity at a point in space as a function of time point in the image as a function of time so we have time series image of intensity before a transformer get a power spectrum and that is what is plotted here power spectrum as you increase the rotation rate of the cylinder so when you have one kind of wave that is rotating around the cylinder you get a single frequency component maybe some harmonics but only one frequency is necessary to characterize the dynamics but as you go higher in rotation rate of the cylinder you reach another transition bifurcation you have a transition in the solution and where do you have two fundamental frequency now you see a lot of peaks in the power spectrum but all of them are combinations of these two like sums and differences of these two frequencies and multiples of those frequencies so there are only two fundamental frequencies we have a doubly periodic flow and then if we go yet higher with the speed of the inner cylinder we see the background becomes noisy the fluid is no longer simply periodic or multiply periodic it is non periodic and this kind of non periodic behavior is called chaotic behavior we'll talk about that further now if you go and rotate both cylinders and start here at thermodynamic equilibrium rotating the inner cylinder you see what I've just described you have this Taylor vortex flow the time independent vortices in this region and then the lighter blue here is where you have the waves that rotate around if you go in the co-rotating frame with these waves the flow is time independent in that rate rotating frame but if you go higher you can get two frequencies that's called waves that are modulated at another frequency gives you two frequency and then you have the chaotic flow but if you rotate the outer cylinder first it's some frequency and then go up you get different kinds of transitions this was a real surprise of it very complex diagram which is still the subject of extensive research both theoretical and experimental research and it was just printed in an annual review paper a few months ago as an example of the complex behavior you have as you drive a system away from thermodynamic equilibrium now turn to another problem Alan Turing familiar to everyone here from the Turing machine fundamental model for computer was thinking in the early 1950s about how to patterns form in biological systems and why does a leopard have spots where these patterns come from well Alan Turing was not an experimentalist he was not a scientist not a physical scientist or a chemical scientist he was a mathematician and he developed a model to address this question and this is Alan Turing's last paper he was he became interested in biology in the early 1980s and Broadway in particular pattern formation in biology and he developed a mathematical model of chemical system where you have chemicals just two chemicals that can react with one another so you have a reaction rate and they diffuse there's no fluid motion no fluid dynamics here just reaction and diffusion only two processes and what can happen as you vary the concentration of the chemicals beyond a certain concentration of the chemicals he found a pattern would spontaneously arise there would be a bifurcation we call it pitchfork bifurcation a transition in the solutions of the equations that would describe this system so he said this is quoting from his paper a system of chemical substances reacting together that's a rate constant and diffusing imagining them diffusing through tissue although it may be originally quite homogeneous may later develop a pattern due to an instability of the homogeneous equilibrium so people began to look for the Turing bifurcation to a pattern and here now nearly 40 years later it was observed it's pretty simple to observe once you know how to do it but not only ourselves but others a long time to figure out how to do a controlled experiment to observe a Turing pattern now this pattern really is arising from a Turing transition a Turing bifurcation it's a transition at which the spots appear with zero amplitude and the amplitude grows this square root of the distance away from the transition that's a pitchfork bifurcation behavior and the analysis gives you a characteristic Turing's analysis gives you a characteristic relationship a wavelength which is related to the diffusion coefficient of the chemical species and the rate constant rate constant for the reaction gives you a time this is a characteristic time so this time was measured in the experiments independently and the rate the diffusion of the chemicals in the experiment was measured separate from the pattern formation experiment and the wavelength here is measured 0.2 millimeters and this pattern that you see here satisfies the Turing relation so this is a Turing pattern and this was done in a reactor where you could bring in chemicals that were oxidizing chemicals and chemicals that were reducing chemicals and two separate reservoirs these are stirred homogeneous reservoirs and there's no reaction in this reservoir and no reaction in this reservoir the chemicals diffuse into a gel that separates the two reservoirs and that's where the pattern forms so you take a picture looking through one of these reservoirs at the pattern that forms in the gel now the analysis that Turing and Taylor took were both of the same type you know the solution for the system near equilibrium you can often in many cases solve and find the state of the system as it's driven away from equilibrium but still near equilibrium it's homogeneous it has the symmetry of the boundary conditions and you can look then at what happens when you have an infinitesimal perturbation of that solution so you have a uniform state and you imagine an infinitesimal perturbation which you always have in an experiment does that perturbation grow or decay so this is the growth rate of the disturbance this is the eigenvalue of an equation that you get when you do the stability analysis that Turing and Taylor did you get the growth rate and the growth rate is negative for situations close to the equilibrium state that is R has some critical value and if you're below that critical value the distance this is distance away from thermodynamic equilibrium then that growth rate is negative for all disturbances but as you increase your distance and you increase away from equilibrium you increase R you reach a critical value of the growth rate at which it becomes zero and there's a characteristic link scale that comes from the analysis at which that happens and you go just epsilon infinitesimally beyond that point and you get the growth rate is positive you get the growth of a pattern spatial pattern you no longer have a uniform state and that's a general type of analysis Turing knew apparently as far as anyone knows he knew nothing about the work of Taylor but the procedure he followed was the same in principle as Taylor followed and many others have followed now okay well this growth rate here sigma the growth rate of the disturbance could be a real number or it could be a complex number if it's a complex number you get traveling waves and here for chemical system you get these waves this is an oxidation front here's another one they are traveling towards one another when they collide they annihilate but that's beyond an instability where you have a complex eigenvalue for the growth rate so you have traveling waves and this particular reaction has been much studied it's called the Belosov Jabotinsky reaction okay well you have these spiral waves in physical situations and biological situations have spirals in the ocean and galaxies all kinds of situations with spiral wave solutions but in the in the heart you have a pacemaker the sinus node here which sends out a signal to the heart to beat electrical signal and it propagates out in the normal heartbeat you have 60 beats per minute or something but sometimes when you have disease the pathway electrical pathway can be broken and then instead of having the regular beating you get spirals forming and these spirals rotate faster than the pacemaker is pacing so they take over and make the heartbeat very fast you have irregular heartbeats and they're very fast tachycardia and then irregular fibrillation and then you die and this happens in the United States to about 100,000 people per year more than 100,000 in the world I don't know many people have this problem with these spiral waves forming in the heart and so they're in medical schools many researchers studying how to interrupt these spiral waves and recover the normal sinus rhythms that you have for in a healthy heart particularly at Harvard Medical School and Duke Medical School if you can give the right external stimulus you can maybe interrupt the spiral waves and return to normal heart rhythm okay here's another problem entirely but it's a system which we drive away from equilibrium you have a container of sand or some particles that you oscillate vertically you can take some particles put them on top of a loudspeaker if you turn up the you set it for some frequency say 25 cycles per second oscillations per second if the amplitude is small and you look down from above at the layer of sand they are particles you see this flat layer just go up and down as you oscillate the speaker now as you increase the amplitude you get a point to an amplitude where the acceleration during a cycle exceeds it for some period of time the acceleration of gravity so the layer of sand leaves the container bottom goes in the air and then comes back and hits and it still goes up and down if your maximum acceleration per cycle is twice that of gravity the layer will go up it comes down you look at it still a flat layer but as you increase the amplitude of the acceleration turn up the gain you reach an acceleration of about two and a half times gravity and look at the pattern and this has been done now by thousands of high school students very simple experiment very cheap you see a pattern will spontaneously emerge here is the pattern that was observed in the square container and you look at one of these white dots there are thousands of sand grains but if you look up close you can see the individual grains this is just a close up here that's a snapshot at an instant of time one oscillation of the container later where you have this pile of grains here you'll get a pile of grains here two oscillations the container later you again have a pattern it's just like this one so this was studied as a function of the amplitude and the frequency and Dr. Mark shot it sitting in the back of the room there who will talk in his sessions about molecular dynamic simulations did the molecular dynamic simulations for this problem where you have particles that are being oscillated up and down and let's assume no air friction actually you can evacuate the system so you don't have the additional complication of air friction on the particles and so the particles just move and parabolic pass between collisions and they collide and bounce off they satisfy Newton's laws in the collision and you can calculate their trajectories in a simulation of the type you will do or you can do if you go to Dr. Shattuck's session and you can calculate the patterns and this is the result of the simulations here for a small container this was done number of years ago so the computer capacity was small so we couldn't handle a huge number of particles smaller number sixty thousand spheres and the experiment was done in a small container too but you see the agreement is pretty good this is a photograph looking down at the experiment and this is image made from the molecular dynamic simulation and that's for a certain frequency of oscillation of the container fifteen oscillations per second now if you change the frequency of oscillation you can get a different pattern this is a higher frequency of oscillation and the pattern is basically one of stripes you see in the small container the effect of walls if you had a big container would be parallel striped pattern and it was found for some condition some amplitude of oscillation some frequency of oscillation instead of having a pattern that filled the container you'd have a localized pattern and this structure captured in a snapshot is shown here at an instant of time but this is a time evolving pattern Dr. Shattuck has made a movie very nice movie and you can see what happens now this is a peak and then a little crater peak crater peak crater as the container oscillates up and down so two oscillations of the container you would have the same pattern one oscillation later you'd have a crater after you started with a peak okay now let's go back to a simpler system not spatially varying in time or varying in space but one that can vary only in time that is we have chemicals that are fed into a reactor which is well stirred so it's homogeneous no spatial variation and you can vary the concentration of the chemicals and look at the concentration of the reaction products now the reaction products are real mess here there are roughly 80 different chemical species in this reactor you're continuously feeding in chemicals they're stirred they react produce many products and they are being emptied at a uniform rate so you can look then at the concentration of any one of the species and one of them that is easy to measure in this particular reaction is concentration of the bromide ion as a function of time so here's bromide ion concentration versus time you see reaction is fairly slow the period of oscillation is fairly slow but it's oscillate and for some conditions you have nice periodic oscillation just nearly a sine wave but certainly periodic in time as you vary the concentration of the feed though at some point you get more complex behavior and this is one situation where the amplitude is varying you see and it looks like it's it maybe has a period that's this size here because this one it looks like it's about the same here but the amplitudes are varying it's not exactly periodic in fact it's not periodic at all and if you look for a transform of this time series you don't see sharp peak car funding to periodic oscillation you see broadband spectrum so that you don't have a well-defined periodicity you have something more complex and one way you could study that is the kind of analysis you might do in some of these sessions you can take this bromide ion concentration at some time T and at some later time and that gives you a point in a two-dimensional space so you have here this point which is this is the bromide ion concentration at time T and this is so you have your your variables x y or just these time t and time t plus tau that gives you a point in a 2d space and you can follow that point in time so you let time evolve and see what the what you have at the next point in time and you get a smooth curve that will describe the dynamics it's called a phase space attractor it describes the dynamics of the system now we can get something yet simpler we can draw a line here and call this the x-axis and the first time we cross this axis we give the value that the we have on the this x-axis x 1 so we cross it here that's x 1 the next time we come around and cross this action we call it x 2 so that gives you a pair of points x 1 x 2 and this map right here in this so you have x n plus 1 versus and you have a particular point x 1 x 2 now now let's look and see what how this evolves in time there's the point now this is taking the concentration of bromide ion as a function of time and converting it into this graph of in two dimensions of this bromide at time t and bromide with some later time tau that gives us a continuous curve and then each time we cross this line we get a point and we see the points are not randomly filling this graph as time evolves we have a graph emerging which is a map of this axis into that axis it's a one-dimensional map and there's some scatter it's real laboratory data but you see it fills out a smooth curve give an x n this smooth curve gives x n plus 1 the system is deterministic yet non-periodic and that's what is the case in chaos and in chaotic behavior non-periodic behavior of a deterministic system where if you have two points that are close together initially you can take any two points close together on different orbits here and look at them they will spread apart exponentially fast so after a while you know nothing knowing the behavior of one curve you know nothing about the other curve because it's spread so different it's completely different so the behavior long-term behavior is unpredictable short-term you can predict you have this deterministic function but the any fluctuations in the errors any differences grow exponentially fast okay so let's look at another type of process growth processes so here we have two glass plates and there's a thin layer of oil between the two black glass plates very thin the distance between the plates is point one millimeter and the plates are in diameter 300 millimeters so the size here three thousand times thickness between the plates and we filled the layer with oil and then we pump air into the center hole so this white is the oil layer and the black is a little oil bubble in the center and then we pump oil into the hole pump air into the hole and you see the air fingers this is called viscous fingers oil is viscous the fluids viscous the fingers grow into the oil layer and the finger each finger that starts to grow will then split and the two new fingers split again and this happens repeatedly and this is a problem that is a problem in Texas why in Texas because for years Texas has had an economy based on oil and you remove the oil from the ground by pumping out the oil something must replace the oil that's being pumped out and that's water from the water table and that water table say is initially flat but as you pump out the oil fingers of water penetrate the oil table and after a while you're pumping from your pump above ground you're pumping water even though there's a lot of oil left in the ground because of this instability so the oil companies paid us to do these experiments because they would like to get more of that oil now we didn't solve the problem but we got money okay okay now you notice this is an irregular pattern and I'm sure most of you or many of you are familiar with fractals dimension which is not integer this pattern is more complicated than say solid surface square or circle one dimensional two-dimensional or what is this well nearly a century ago in the 1920s Lewis Frye Richardson an Englishman wanted to compute the length of the coastline of Britain so he took a map and he took a rule of a certain length scale and measured the coastline say with a length scale corresponding to 200 kilometers and he got a certain length and he said well let me take a finer scale because I've got a better map than this this doesn't approximate my map very well so he took 50 kilometers and the length was larger and so on you took smaller and smaller scales and then plotted the result of log log scale and concluded that the coastline of Britain was not one-dimensional and it wasn't two-dimensional but it was something that was not an integer dimension 1.25 now not much work was done on non-energy dimensions until the 50s when some mathematicians for mathematical reasons began to be interested Rania and others in non-energy dimensions but it didn't enter the physical science world until later Mandelbrot began to study non-energy dimensions and he gave the term fractal to mean non-energy dimension and in fact the dimension for the soil pattern is 1.71 okay now we also did some experiments on an electrolyte zinc sulfate between two electrodes and if you close the switch here that close the switch you grow a pattern that is fractal and it has a dimension also 1.71 and and so one can look at ways to characterize these spatial patterns that are fractal or are dynamical systems which have phase-space attractors which are non-integer and that was done in a series of papers so more recently studied the growth of bacterial colonies this is a colony of bacteria bacillus subtilis and rod-shaped bacteria seven micrometers long about a micron in diameter and they have flagella which rotate and propel them so they're multi-bacterial and you can see them moving this is looking with a microscope you see the rods as they swim and now you put a drop of the bacteria maybe 10 bacteria in a five microliter drop or maybe 10 million bacteria doesn't make a difference you just start with a small droplet with some bacteria in it and they multiply grow and multiply because there's nutrition in the gel this peptone some when you make the gel you mix in some protein that the bacteria like to eat and the little drop of bacteria in the liquid will grow into a colony and here's a picture of the colony this is a different bacterium penipacillus dendritiformis doesn't matter it's another rod-shaped bacterium and you see this pattern interestingly has the same approximately the same fractal dimension now this is a hands-on school so it's time for a hands-on experiment that everyone can do let's see here have some pieces of a garbage bag for my office so this is University of Texas standard trash bang and let's see everyone should take one of these and we'll do a hands-on experiment together okay don't do anything yet but do notice except to notice that one edge has of the square plastic sheet has a little cut in it now this plastic sheet is about 10 micrometers thick 12 micrometers thick doesn't matter you can do this with a plastic sheet of varying thicknesses that's not critical at all wait till everyone gets a sheet so take the side with a slit in it and put it up and then hold the sheet between your two hands firmly and then we're going to tear the sheet in half you can do it slowly so that you tear it let the tear go right down the middle okay does everybody have a sheet you have one in the back okay we'll be doing hands-on experiments for two weeks this is numero uno number one experiment alright so now just pull slowly and tear the sheet into two pieces now I want you to look at the edge of the sheet look with your neighbor talk to the person next to you look at the edge of the sheet and describe what you see just looking at the edge looking at the edge okay what do you see describe it to your neighbor okay anyone what do you see yes ma'am like you think it's a fractal do you see waves within waves within waves right that's characteristic of a fractal well let's look here so this is photograph made with an ordinary camera nothing special here a cheap camera you make a section 30 millimeters long that's what we see now you see this little box up here on the left the little rectangle let's just magnify that all right magnify 3.2 times and it kind of looks like the original pattern and let's do it again and again and again now you begin to see a thickness here I said the sheet was 10 microns thick this is 250 microns maybe it's a little more than that and here we're this is 80 microns micrometers here now you see the thickness of the sheet but you can see waves within waves you see this fractal cascade and you calculate the dimension happens to be 1.7 I don't know why very simple experiment published in a magazine you've probably heard of okay and there was some theory done by my colleagues Michael Martyrs professor who works in condensed matter physics and only dynamics and he has a textbook graduate textbook condensed matter physics is for those of you in physics and he looked at different stretch rates so if you measure the amount of stretch at the edge relative to the original separation between two points so you take two points in the original sheet and see how far apart they are after the sheet has been torn and in this case here the blue dots go to a separation 1.8 times the original separation and this this is actually analysis theory not experiment but we have similar curves from experiment now if the spreading rate near the edge is fast enough here he found so like this curve blue here you get the fractal waves within waves within waves and if you go to the market and look at it's some leafy vegetables like kale or some other leaf vegetables you will see you can measure the fractal dimension of them they you see waves within waves within waves so if the growth rate at the edge of the leaf is fast enough you get the fractal other leaves don't grow quite as fast and they may have two different frequencies now if you take the waves on the edge you analyze that do a Fourier analysis you find two waves are present for this growth rate right here if it's this is the growth near the edge and if it's slower you may have on like some lettuce leaves have just one wave but they're good number of plants and you can see this in flowers also some cases where you have the fractal it where the growth near the edge is sufficiently fast and in fact here's a violet flower and this has waves the fractal cascade lettuce leaf plastic this is looking at the edge and this is looking from the side now what if you take a trump a cylinder and let the end grow so this was done by Iran Sharon it had a polyacrylamide gel gel that was a cylindrical shape you dip it in water and expands and depending upon the amount of expansion you can get something that just expands and looks like a trumpet faster growth rate you get one wave yet faster growth rate you get a daffodil okay you get something with fractal character so we have these different fractals is there something universal about them we go back to Newton of course and he was thinking in that year 1666 the University of Cambridge was closed there was a plague in London and they closed the University of Cambridge it closed all universities because many people were dying 25% of the population of London died and they sent the students and professors home Newton was a young instructor in 1666 and he went home and he was sitting in his yard looking at an apple tree now this is apparently a real a true story it's written by four different he never wrote about it but four people who were acquaintances of yours or friends of his wrote this story that he told them that thinking about the apple falling he said well the the apple must be attracted to the earth well the earth is a sphere why does it go straight down he's think well it's attracted to the right by that part of the earth in the right side and to the left but must be attracted towards the center of the earth and if the apple was attracted to the earth the earth must be attracted to the apple so there's a universal attraction between any two masses near the earth's surface and then decades two decades later he began to think at least more than one decade well if this attraction between two masses on the earth is it universal does it occur over all length scales to the furthest orb of the universe he said could it describe the planets being attracted to the sun and he by that time had his equations and worked out the trajectories of the planets the universal law of gravitation so this idea of universality has developed in particular by Newton is one that guides much of what we do in science now we work in different areas of science but we find similar types of phenomena in many different disciplines and that's the situation here what whether this is some universality that is yet to be fully understood but you are guided in our thinking by looking at different kinds of phenomena which might have a common description now what about the problem I think I better stop where is my should I stop there uh yeah I started late keep going I'll go quickly so here are birds that are starlings this is Rome and every winter millions of starlings flock along the Tiber River in Rome and they form these wonderful patterns which are really quite well-defined flocks and this group of Italians looked at these bird flocks and made movies and they're still analyzing these movies but they they made using multiple cameras they could track now every starling looks pretty similar so you have to have many cameras to keep track of a given one but they kept track of the of as many as 10 000 starling in a flock and they looked at the correlation as a function of flock size flock size and they found this simple relationship so applied the same type of analysis to the bacteria now the bacteria are moving in two dimensions not three much simpler and they are moving at very low Reynolds number so inertia plays no role the birds have inertia they can fly and the coast at the bacteria move in two dimensions and they their interaction is quite different because of the difference in size and speeds and you can see them move and you look through a microscope and a movie and you can look at the velocity and these arrows represent the velocity and we say that the bacteria are in a cluster if their velocity vector if they're close to a neighbor who has the same direction and magnitude of the velocity so you see that cluster formation is very dynamic bacteria joining a cluster and maybe in a cluster all the time and you can see it's advantageous to be in a cluster you're not in a cluster you don't move very fast these not in a cluster move about one micrometer per second a cluster moves typically 30 micrometers per second so if you're going for nutrients or going to escape a toxic chemical then it's better to be in a cluster and we did the same type of analysis as for starlings here the green curve is for the starlings and you see the bacteria give the same kind of curve so i'm done so let me just say okay we have different examples from inexpensive tablecloth science phenomena in nature that we can characterize using the kinds of tools we'll discuss during the next two weeks thank you