Welcome to this final week of the course. In this week, we will be looking further into the modelling of our data, the extraction of physical parameters. As you may remember, we start out in our 3D analysis with the data acquisition step, we then, from our acquire projections, reconstruct the 3D volume of our material, which is then segmented and meshed to create a geometrical representation of our structure, and this is then what we analyze in our final modelling step. You may know that very often, freely analysis is working towards the end goal of visualization where you get a 3D rendering of your object or material that you can examine and draw some qualitative conclusions from. This is what you will often see in medical scanning, CT scanning in the clinical world, where the images or 3D reconstructions are evaluated purely on a qualitative basis from visual representations. But in material science, we are very often interested in getting actual numbers representing the fiscal parameters describing the properties of the material. To this end, we have various methods going from the most simple geometrical measurements of the structure that we have derived to more advanced modelling, and we will cover everything in this final week. To begin with, it's possible to get some quite good representations in numbers of your material from very simple measures, and this is something that [inaudible] will explain in more detail. One of the simple properties is the one we call porosity. So, how much air volume do we have compared to the full volume of the sample? This is in principle after we have the segmentation stuff just counting how many voxels do we have in the whitespace or the pores, compared to the total number of voxels. The material that [inaudible] was referring to in this case is of course our experimental case of the North Sea Chalk, where we are very interested in knowing the absolute porosity of the material in order to understand how liquids and gases may interact with the material in a natural setting. Another example which takes such an analysis step further is from a technological material from the field of solid oxide fuel sells, where also this aspect of how gases may enter the structure and how it may percolate foods structure to reach certain active sites in the material where reactions can take place, is of interest. This is something that we also use some relatively simple measures to quantify. For example, we have a term which is called tortuosity. It can be understood from looking at this relatively simple figure here, where you can see that you have a source of your gas molecules in this case, that may percolate through the structure to reach the destination sites where reactions may take place. We are of course interested in how efficiently these molecules can percolate through the structure. Something that has an impact on this is this measure of tortuosity, which is a measure of how far the distance, the path that the molecule has to travel through the structure is, compared to the direct line of transfer. What is done here is then to calculate simply the distance along the percolation pathway from the destination site to the source, and calculate the direct distance and then do normalization to that direct distance. This is then your tortuosity number, which is a simple scalar that describes how easily the molecules can reach the destination sites. Another measure, which is relatively simple to extract for such a structure here, is what is called a critical pathway thickness. So, that is a measure of how constricting areas in the percolating pathway may restrict access of molecules to the destination sites, and this can be modeled by taking the 3D network that we have determined from our measurements, and then gradually shrink it, so add a lining so to speak of material to the inside of the porosity, the percolating pathway, and then determine at each shrink radius, at what point certain pathways become non percolating, meaning that molecules can no longer reach the destination sites. So, this is a relatively simple way of finding again, a symbol number that gives you a quantitative measure of how easily molecules may percolate to certain destination sites, and this can be again visualized in this way where you can see another example of the percolating pathway to the destination site, and here, the critical radius symbolized by this small red sphere, showing you that this is the size where molecules can no longer, for example, percolate to the destination side. As you have heard, we can extract physical parameters from very simple geometric measures where we don't make any assumption about how the material behaves or the interaction between, for example, a gas and the material, or we can go to slightly more advanced modelling as we discussed here for the solid oxide fuel case where it is in principle, some simple geometrical measures that we are taking again, but we are making also some model assumptions that, for example, the percolating pathway boundaries are hot. So, there we are applying some assumption of the physical model for the system. Finally, when we go to very advanced complex physical parameters that we want to extract, we cannot directly take these parameters from our geometrical structure alone, we need to establish some model that describes how, for example, a liquid will interact in terms of reactivity with the boundary walls or it can also be, for example, how the mechanical parameters will behave in a composite material like for the wind turbine case, and here we can use a method like finite element modelling, which is what we will be focusing on in the remainder of this week.