Treffer: Subset Geometry

So far, we have studied the geometry of the percolation system. Now, we will gradually address the physics of processes that occur in a percolation system. We have addressed one physics-like property of the system, the density of the spanning cluster, and we found that we could build a theory for the density P as a function of the porosity (occupation probability) p of the system. In order to address other physical properties, we need to have a clear description of the geometry of the percolation system close to the percolation threshold. In this chapter, we will develop a simplified geometric description that will be useful, indeed essential, when we discuss physical process in disordered media. We will introduce various subsets of the spanning cluster—sets that play roles in specific physical processes.