 We start the afternoon session. I'm the chairman, Annalisa Fasolino, and the first talk we will try to keep the time because we have to be ready at 7.30 for the bus. So the first talk is Bo Persson, Heart Particle Addition, and on the stability of spinning asteroids. Very original title. Okay, thank you very much. I'm also very happy to be back here. I was here the first time 1978, I think, or was it 79 or 78? 79, yeah, so very long time ago. Here you asked me to say a few words about my Grubbins because I think I have interacted with him longer than anybody else here. And my initial interaction was not particularly good. So it was around the beginning of the 1990s. We were both interested in trying to understand the measurement of Jackie Crimm. She did some quartz crystal measurements where she slide absorb layers on metals. And Mark Robbins and company wrote a paper where they tried to explain this by the corrugation of the substrate, exciting phonons or vibrations in the sliding layer. I had a different background coming from having studied electronic friction. And I knew that the lifetimes or sleep times Jackie was measuring are very similar to what you can deduce from surface Earth's stability measurements. So when Mark had written this paper here, I wrote a comment which I tried to get published in Science 2, but it got rejected. But still it got Mark very upset for some years. But as time goes on, we finally become friends again and we even have some common papers. So happy ending my say of this story. So I will tell you about some work very recent. I've done this year basically on adhesion and heat transfer in asteroids. And the reason I did this is that one astrophysicist contacted me and asked if I can help them to understand these problems. This has been started already by astrophysicist for maybe 20 years, but they used very simple models, which really doesn't work for these applications. I will tell you a little about first adhesion for elastic stiff particles with surface roughness. And application will be to stability of spinning asteroids. And then I will tell you about some experiment I did myself about capital adhesion which tests some part of this theory. And then I will speak about heat transfer in small particle systems and application to asteroids again. So the asteroid belt was formed at the same time as our solar system. So it's very old, 4.6 billion years old. And the temperature in the asteroids is around 200 Kelvin typically. And at this temperature and over this time period here, basically all molecules which are absorbed on the surface will get desorbed, will disappear. If the binding energy is below one electron volt. So these particles here are very clean. At least that's what I assume. So you cannot form any capital bridges between them. And I will assume that there is just fundamental interaction between the fragments in these asteroids. And this is how an asteroid typically look like. They are called rubble pile asteroids. They consist of many fragments. And the size of these can start at 10 meter lateral size down to micrometer. You can see this region here seems to be full of very small particles. And the interesting thing is that these asteroids are rotating and the rotation speed changed with time because of photons absorbed from the sun. The photons have some momentum and that will change the rotation speed of the asteroid. That is slowly of course, but on the time scale of 10 million years, they start to rotate so quick that they typically break up into pieces. Which cannot be studied directly because it's 10 million years between each such event. But here is very interesting information about the rotation speed. Here is plotted figure with with the rotation period in hours. No logarithmic scale as function of the diameter of the asteroid. And you can see that basically all at least all the bigger asteroids, no one rotate faster than 2.3 hours. That's the shortest rotation period. And this is exactly what you get if you assume that only gravitational forces keep together the asteroid. If you look at the particle on the surface of the asteroid here, on it act some forces, a centrifugal force, gravitational force, and maybe some adhesion to particles in the neighborhood of it. So at the point of just this particle being able to fly off, you must have this force equilibrium shown here. And if you just put in, we know how the gravitational force look like, its function of the radius of the particle. We know how the centrifugal force look like. So if you just use this equation, you can show that the rotation angular velocity at break up is given by this equation here. So if you neglect adhesion, it depends only on the gravitational constant and the mass density of this asteroid, which are known. And if you put in those quantities here, you get a period 2.3 hours, just like you see experimentally. That means that this addition term here must be very small. And I'm going to show you that when you have very rough particles, rough surface, the addition does not depend on the radius of the particle. And the only way you can explain these results here is by assuming that the addition force between the particles is of order nano-neutron. You assume that then you can explain why no one is rotating faster here. And you can also explain why some small asteroids can rotate faster than these 2.3 hours. Because if you take into account this addition term, which depends on one of the radius here, for small radius this becomes important. And that can explain why you can see longer life, longer rotation, shorter rotation period than 2.3 hours. So I will try to model the addition between fragments of stone, of minerals. And so the first thing we did is that we took a granite stone and we cracked it. And I measured the power spectrum of this granite particle, granite surface. And with my stylus instrument, I can only do that down to micrometer roughly. So this region you see here is the power spectrum of a granite surface. It has brought the logarithm of power spectrum as function of logarithm of wave number. So 10 to the 6 equals 1 to roughly micrometer roughness. But the particle, which I can simulate on a computer, are much smaller than this. So I assume that the power spectrum can be extrapolated like indicated here. And then I do calculation for particles with different sizes. And the shortest roughness included is of order nanometer. And then depending on the size of the particle, maybe I can do something here. Do I need to close it and start again? Or what do I need to do? I need to put in that number again. Okay, moment. I have to get it. I don't like the stupid systems 0, 8, 3, 7, find 3. Can you join without the video? Okay, moment. I need to find out here. I'm back. Okay, good. I think I finished that page. Yeah, so I'm looking at particles with different sizes. And the longest wavelength roughness I can include in the calculation is determined by the lateral size of the particle. So when I look at particle with increasing radius, I need to move this cutoff to longer wavelengths or shorter wave number. And I generate random rough surfaces by adding plain waves basically with random faces and a weight which depends on this power spectrum. And here I show you one figure. This is a randomly rough surface which I've generated and now I add it on top of a spherical particle. And I consider two different cases, one when I have fundamental interaction in between and I assume there is an adhesive pressure which scales like 1 over the distance to that 3. And the other case I will study is with capillary bridges. So then I have liquid in some region at the interface and I get negative pressure because I assume this liquid will wet the surfaces. So when I do these simulations, I get a different addition force for every particle because every particle have a different radius, different roughness. So for each particle I do average over 60 different realizations of this roughness. And this figure here shows the cumulative probability to find some particular addition force for fundamental interaction and for capillary bridges. You can see for fundamental interaction it's of order nanometer or little less and nanonewton or little less. And for capillary bridges you get about 100 times bigger adhesion. This figure down here shows the addition force as a function of the radius of the particle on a logarithmic scale. If you have perfectly smooth particle that's indicated by zero here, no roughness at all, then you can apply JKR theory or DMT theory and you expect a linear dependence of the force on the radius of the particle and that's this line here. It has slope one on this logarithmic scale. And if I take granite which is indicated by one here, I get an addition force which is independent of the particle size. So one nanometer particle will give you the same or the addition between two nanoparticles is the same as between two blocks which have 10 meters diameter. And these numbers here is when I scale the roughness on the granite particle. So here I make it smaller and smaller. Here it's only one tenth in amplitude compared to the real one and you can see how you approach this linear scaling when you reduce the roughness. But really for roughness on mineral particles you are down here so you expect no dependence on the radius of the particle. We started the same for capillary bridges and you see basically the same thing. The force is independent of the radius of the particle as long as you have enough roughness and when the roughness goes to zero, smooth particle, then you have again a linear radius dependence. This figure only illustrates the stress which acts between the particle and the substrate which in this case was a flat surface. This is for capillary bridges and this is when you have a van der Waals interaction and here is distance nine nanometers. You can see you have a very small contact region and the local stress is not particularly high. It gets 150 mega Pascal here and this material which I'm using corresponds to silica and then you need five giga Pascal in order to plastically deform the material. So you have only elastic deformation in this application and the same is true when you have capillary bridges and here shows the elastic deformations which you will have when this particle is lying on the surface and only interact with this adhesion. And you can see the biggest displacement when the van der Waals interaction is only about 0.01 nanometer, 0.1 angstrom, very, very small. Capillary bridges you get a little more but still very small and that's because the adhesion force is very weak. After it we have only indirect test of this theory but I also did some test of the theory for capillary bridges and this I did myself. I crunched some granite stone in this mortar here. I put the powder on a gloss plate contained in this box here and I changed the humidity in this box by having either a glass of water or salt absorbing, immediate absorbing salt and then I keep it inside for 24 hours. I take out the gloss plate to turn it up and down and all the particles which are more heavy than the adhesion force will fall off so the biggest particle remaining will be those where adhesion force is exactly the same as the gravitational force. And by knowing the size of the particle which I can find using optical microscopy I can estimate the gravitational force and therefore also the adhesion force. And when I have small humidity like this case here about 20% humidity, relative humidity then the biggest particles absorbed are very small of order 100 micrometer. And when I increase the humidity bigger and bigger particles can keep attached. And finally when I reach very high humidity no particle falls off and this happened to be the biggest particle on the surface. So here I plotted the logarithm of the adhesion force, the function of the relative humidity obtained from these kind of measurements. The red line is what I calculate theoretically and the green data plot points are for measurement of the type I just showed you. When I have many symbols that means I have looked at many of the biggest particles on the surface. There's many similar big particles and so that's why I got these statistics. And one interesting thing here is that the theory is calculated for particles with a diameter of about five micrometer but the experiment is involving particles about 100 times bigger. So this also illustrates that the adhesion force is independent of the size of the particle as I already told you. So my second part will be about heat transfer in asteroids which is maybe the most important method used to study some properties of the asteroids is by looking at heat radiation. So this is one asteroid when you look in optical microscope and this is when you look at the heat radiation coming from it. And you can see the temperature goes up to almost 300 Kelvin, the highest temperature. And when you want to study this theoretically you need to know the heat conductivity of this material. If the heat conductivity is very high then the temperature has temperature, surface temperature will be lower. The temperature will diffuse deeper into the material. I mean this asteroid is rotating so this hot region will after a few hours be on the backside where it is very cold. So the temperature you mess your experimentally will depend on the heat conductivity. And when you analyze data like this you need a heat conductivity which is about 100 times smaller than using the bulk material which you have here. And the reason for that is that the heat, the thing which reduce the heat transfer is a contact. So heat diffuses very quick inside each particle. So each particle has an internal temperature which is more or less constant, it's the same everywhere. But different particles have different temperature and there is a heat resistance at the interface. And when you don't have capillary bridges and when you have no gas in the surrounding the particles the only way the heat can go from one particle to another is via the eye of real contact or via the electromagnetic field which you have in the non-contact gap. And I will show you that this electromagnetic field is actually the most important one. And people speak about the heat conductance which is, heat conductance times the temperature difference gives you the energy flow per unit time from one particle to the other particle. So I will focus on this heat conductance because from that you can calculate the heat conductivity. And the contribution from eye of real contact eye claim is very, very small. And the reason is that you have very weak interaction between these particles. And when you have very weak interaction you can calculate the heat conductivity, heat conductance using this equation here. Boltzmann's equation times like a friction coefficient here which I call eta. And this friction coefficient is given by spring constant. There is some interaction potential between the two surfaces here. And if you expand that to second order around the equilibrium position you get an effective spring constant. And that's what is, that's what is K is here. And rho is just a mass density. M is the mass of an atom or in this case maybe silicon dioxide group. And C is the sound velocity. And if you apply this equation you get very small heat transfer like 10 to minus 12 watt per Kelvin for this heat conductance. And that's about two order minutes smaller than I will show you coming from the electromagnetic field. And the electromagnetic field can, depending on separation between two surfaces, you can have two different contributions. One is just radiation of photons gives a very well-known expression for the heat current which depends to the temperature to the four on this solid, on that solid. But if the surfaces are very close to each other you have also evanescent electromagnetic field. And this contribution at short separation becomes much more important than the radiative contribution. And the way you understand this decaying contribution is by that something like that exists. If you look at the wave equation and if you put in a plane wave like this you solve it. You get this dispersion relation and you can solve for the normal wave vector, wave number. And it's given by this equation here. And so if the parallel wave number is larger than light velocity times frequency then this becomes imaginary. And if you have a imaginary case set you have a damped, exponential damped wave. And so that's this contribution. So if you look at the blackboard radiation propagating photons it's given by this very well-known relation here depending only on light velocity, Planck's constant and the Boltzmann constant. And in my case the temperature difference between two particles is very small so we can expand this term to linear order in the temperature difference between the two particles. And that gives you this expression for the heat conductance where A0 is some cross-section area of the particles, of the one of the particles. The contribution from evanescent waves is a little more complicated. It depends on the reflection factor for electromagnetic waves against these surfaces. And here enters a distance. Here's an integral of a wave number. And this factor pi here depends on temperature given by this expression here. And this is reflection factor. So I calculated this expression for silica. Silica has two strong optical phonons. And you need optical phonons to get infrared activity to the material. So here's plot in the manner part of the dielectric function as function of frequency. So here is one high frequency, optical phonon here is one lower frequency optical phonon. And if I use this dielectric function I can calculate this conductance, thermal conductance is given by a function of temperature divided by the separation to the square. And this function of temperature looks like shown in this figure here. So if you would put in nanometer separation, here you would get this factor would give you 10 to the 18. So you have to multiply 10 to the 18 with 10 to the minus 13. You get something much bigger than the black border radiation I told you about before. So now I took, now of course when you have these particles you don't have a constant separation, but the separation varies over the surface of the particle. So I have just averaged this expression again over the different separations which you have in different region of the particles. And here is plot in the Cumbulon probability gain, but now for this heat conductance. And in this case there is some radius dependence. It's it's relatively weak, but still there is some radius dependence that comes because this heat conductance depends slower on the separation than van der Waals interaction. Van der Waals interaction was going like one over distance to the cube, but this goes like one over distance to the square. And that means that farther away from the contact region will matter for the heat conductance. And you can also see it here, it's plotted the logarithm of the heat conductance, the function logarithm of radius. And this is what you get for silica or actually granite particles when you have one here. This is the result you would get if you have perfectly smooth particles. And this line here shows the blackboard radiation given by this initial equation I showed. Stefan Boltzmann, I think it's called Stefan Boltzmann's radiation law. So you can see up to at least 10 micrometer the near field decaying electromagnetic wave is more important than the blackboard radiation. We also studied this as a function of the factor dimension, but I will not go into that. This is my last view graph. This project is still ongoing, so it's not really finished. But one can show that this heat conductivity, which I told you about in the beginning, is given by this heat conductance divided by the radius of the particle times an numerical factor of order unity. And if you look at the blackboard radiation, it depends on the gear depends as a square of the radius because it depends on the area. The photons doesn't decay, so it doesn't matter what separation it is. You get this out of the square dependence. If you look at the contribution from the non-radiative evanescent waves, it depends very weakly on the radius. I already told you that. And the contribution from the area of real contact does not depend on the radius of particle at all. And we are using these results now in equations like this to try to understand the heat conductivity of asteroids. The problem is that asteroids doesn't consist of particles with one radius. I have a distribution of radius starting at, I told you, 10 meter down to micrometer probably. And so we need to develop some theory which can take into account this distribution of particle sizes, maybe an effective medium theory to handle that. Okay. So the paper is open for questions. Here we have one. Just maybe an naive question, but you talked about heat transfer, but that heat may have seen equally wrong with the vacuum that is very cold. So how that heat is being generated somewhere? The heat comes from the photons of the sun. That's the heat source. The asteroid is on the average in equilibrium. So all the energy which gets absorbed by the sun gets emitted as heat radiation. You said this van der Waals force is like nano-Newton and it's independent of the radius. So I mean, I take a block of granite of one meter or the diameter, it will have a nano-Newton. That's surprising to me. This is off. Because if you have a huge interaction in both cases, what is happening out here doesn't contribute. It contributes in a negligible way. So everything which might have happened very close to the contact point. That's why you got this. But it can be that you have like not only one, maybe a few of these contacts. I mean, it's an order of magnitude, I guess. But in principle, you are right. In reality, probably there's three contact points like that. Because at least if you have also some gravity, it cannot balance on top of one sphere. So probably three. So you have to multiply these four calculate with a factor of three probably to get more. But otherwise, this is what comes out from rigorous calculations. So it is like it is. Heat conductivity would be much smaller if they were not rotating because then you wouldn't have this exponentially decaying channel. No, it has nothing to do with the rotation. Because to become an exponential, you needed to have a difference between the rotation. Ah, you are speaking about the first part of my presentation. Yes, the rotation speed of the whole asteroid is changing in time. Yeah, it's changing in time. And basically either speeds up or slow down because of absorption of photons. It depends on the shape. That torque depends on the shape of the asteroid. So for a spherical asteroid, there would be no such effect. But no asteroid is perfect. Okay, very interesting. I think people have to think a bit about that. You will get lots of questions there. So I invite the second speaker.