We present a model of percolation mimicking the self-healing dynamics of a smart grid. While in the case of random graphs it is possible to work out an analytic solution, in the case of two dimensional networks we must resort to numerical simulations. Our findings hint that for planar lattices duality plays a key role yet to be understood. Finally, by to tackling the problem of being connected to a source node, we find the existence of two separate solutions that we study by applying cavity methods and recursive equations.
Self-healing percolation
Antonio Scala
2015
Abstract
We present a model of percolation mimicking the self-healing dynamics of a smart grid. While in the case of random graphs it is possible to work out an analytic solution, in the case of two dimensional networks we must resort to numerical simulations. Our findings hint that for planar lattices duality plays a key role yet to be understood. Finally, by to tackling the problem of being connected to a source node, we find the existence of two separate solutions that we study by applying cavity methods and recursive equations.File in questo prodotto:
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