Percolation around us

The ignition probability p depends on the distance between the trees, the size of the trees, and on how dry the season is. Depending on these conditions, there are two possible outcomes resulting from Smokey s carelessness  

Another problem related to percolation and analogous to forest fires is the spreading of a disease in an apple orchard. In an orchard, the trees grow on a regular lattice [Fig. 6.10(a)]. A sick tree can contaminate its neighbour with probability p. Just as in the above example, for small values of p the 

Consider a substitutional alloy A with A and B atoms randomly occupying sites of a regular lattice (see Fig. 6.11). A B cluster is defined as a set of neighbouring B atoms. For low values of the fraction q of B atoms in the Ai B alloy, the B clusters are small. With increasing fraction of B atoms, B clusters become progressively larger and above some critical value 

Note that for q qc only A percolates, for q q —q both A and B percolate, and for q 1—qc only B percolates. Copper and gold form 

We have given four examples of connectivity transitions described by percolation models. Other examples include the conductor-insulator transition for a random resistor network, oil recovery through a porous 

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