Percolation, Gelation and the Metal-Insulator Transition

And by perfect coincidence, this is exactly the exponent we obtained by screwing up balls of paper But what better model for a folded, solid membrane than a screwed up sheet of paper  

The second feature of the clusters we obtain is a very wide distribution of sizes. Studies have shown that this distribution varies in a quite characteristic way. Indeed, if we call P N, e) the probability of finding an Al-site cluster, i.e., the concentration of A -site clusters, at a distance e = p — Pc from the threshold, we find that 

It is interesting to examine the diminishing power law and its exponent t more closely. In fact, it is not independent of the fractal dimension i perco of the clusters  

Polymers with a branching structure and composed of a great many monomers can thereby be generated. When the fraction p of NCO groups having reacted with an OH group exceeds the threshold Pc, there exists a giant polymer whose size is only limited by the dimensions of the reaction bath, i.e., the reaction vessel. 

The above discussion concerns finite clusters. We have seen that the percolation threshold is characterised by the appearance of a spanning, or percolating 

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