Transport Exponents in Percolation

Abstract

The author investigate how forms and, more specifically, randomness in geometry as found in percolative structures, govern the macroscopic transport behavior. In the first part, they show how in the node-link-and-blob picture of the percolation infinite cluster, one can derive bounds for critical exponents. This method can be used for scalar transport, for elasticity, or for the specific problem of 'continuous percolation'. In the second part, they give an upper bound for the elastic critical exponent which may well be an exact relation (conjecture)