A porous stone in a bucket of water…Thursday, December 22nd, 2011 by Antonio Manzalini
“Suppose we immerse a large porous stone in a bucket of water. What is the probability that the centre of the stone is wetted?” This is how Geoffrey Grimmett begins his book Percolation.
Percolation is a mathematical theory dealing with fluid flow (or any other similar process) in random media. It is a theory of great theoretical importance in diverse ﬁelds as biology, physics, and geophysics. Amazingly I’ve just learnt that it may have an immense practical importance in the context of future networks.
Imagine a network as a…porous stone immersed in a in a bucket of water! Let’s make an example, very much related to Roberto’s post of 20th December. Consider a wireless networks composed by an large number of communication entities interacting with each other by overlapping their communication halos. Imagine also we wish to find control algorithms based on local decisions, adaptive to local changes, aiming at guaranteeing full connectivity and efficient routing in this meshed network.
Well, this paper (by Caltech) solves this complex problem, in an effective and elegant way, by using (a variant of) the Percolation Theory.
This is to me a nice example how breakthroughs involve crossing diverse scientific disciplines and finding new way of solving problems with methods developed in other contexts.