Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Percolation processes

I. Crystals and mazes

S. R. Broadbenta1 and J. M. Hammersleya2

a1 United Glass Bottle Manufacturers, Ltd

a2 United Kingdom Atomic Energy Research Establishment Harwell, Near Didcot, Berks


The paper studies, in a general way, how the random properties of a ‘medium’ influence the percolation of a ‘fluid’ through it. The treatment diifers from conventional diffusion theory, in which it is the random properties of the fluid that matter. Fluid and medium bear general interpretations: for example, solute diffusing through solvent, electrons migrating over an atomic lattice, molecules penetrating a porous solid, disease infecting a community, etc.

(Received August 15 1956)