 We're ready to start again with our next talk by Professor John from Prospect. Welcome. Okay. First of all, I'd like to thank the organizers, Professor Hyun and Professor Jo, to making this nice school and workshop. So today I'm going to talk about the diffusion of the propyl particles which interact with polymers. So this is the brief outline of my talk. So I give you some very brief introduction of active Brownian particles and active scholastic system. Then today I mainly give you two topics. The first one is that when this active particle is strongly connected to the polymer network. And the other topic is that when this active particle is embedded in the polymer network and what's going to happen. Okay. So in the morning, Professor Yong-ju Baek gave a very nice introduction about the self-propelled particles. So I think that I can actually skip this slide, but I just only point out one thing that this self-propelled particle is some particles which having the kinetic motion which doesn't satisfy the so-called fluctuation, this space and cell. Which means that there is some additional or thermal energy which that particle can actually consume to having some strange motion. So that in the mornings we learned about these micro-streamers and then these micro-streamers give a long and tumble motion. And then there's other examples so-called like a Janus particle or active colloid. So you can see that it is conventional colloid but we have some spatial treatment at only half a sphere. So we coated it with a platinum and then when they, in this solution then they have a chemical reaction then it has some directional motions. Because of that it has looks like some living particles. And obviously inside the cell there are many cases that it shows some active particle motion which mainly by this ATP related motor protein. So this is some very essential of this what people call active Brownian particle. As you know that you imagine that you have one colloid particle like that and then this particle have two actually motions. So one is the translational and the other one is rotation. But in this case that when this active particle, I mean this Brownian colloid having some directional like a propulsion with the velocity bp then actually you can see that their rotation and the translational motion is coupled each other. Because of that it has actually some directed motion. Imagine that if the rotation is very, very slow then you see that the particle because it has some directional propulsion so it can go some directional motion. But if the rotation is very fast it can actually very fastly lose the memory. So there is some coupling between them. So if you analyze in this equation then you see that actually this directional diffusion can be given by this picture. So you see that the average step length can be the self-proposant velocity times this memory time tau a and this tau a is actually the inverse of the rotational diffusivity. So I can give you the simulation of this active Brownian particle. So here we can also define how this active motion is strong. So what we call this Peckley number is just a measure to quantify the activity of the particle and then this Peckley number essentially you may be considered that some ratio that this active mobility divided by the thermal mobility. So it is one means that it is like thermal motion and active drift is the same. So it's larger than one then that means that this activity is higher than the thermal. So you see that when Peckley number is zero that the black one so you see that it shows an ordinary Brownian motion you can see like that and then if we are adding this activity to the self-proposant dynamics then now you see that it shows a directional motion. So it looks pretty different. And this is some experiment done in the French group and then they did a very interesting experiment. So they did the parents sedimentation experiment for active colloid. So inside of this vessel there is an active colloid particle and then now we have a gravity so that you see that there is some balance between this concentration of the particle and then the height because of force balance between this gravity and then. So here they show that so you see here the first of what you see there.